Given a set of squares and a strip with bounded width and infinite height, we consider a square strip packaging problem, which we call the square independent packing problem (SIPP), to minimize the strip height so that all the squares are packed into independent cells separated by horizontal and vertical partitions. For the SIPP, we first investigate efficient solution representations and propose a compact representation that reduces the search space from to , with n the number of given squares, while guaranteeing that there exists a solution representation that corresponds to an optimal solution. Based on the solution representation, we show that the problem is -hard. To solve the SIPP, we propose a dynamic programming method that can be extended to a fully polynomial-time approximation scheme (FPTAS). We also propose three mathematical programming formulations based on different solution representations and confirm their performance through computational experiments with a mathematical programming solver. Finally, we discuss several extensions that are relevant to practical applications.
{"title":"Packing squares independently","authors":"Wei Wu , Hiroki Numaguchi , Nir Halman , Yannan Hu , Mutsunori Yagiura","doi":"10.1016/j.tcs.2024.114910","DOIUrl":"10.1016/j.tcs.2024.114910","url":null,"abstract":"<div><div>Given a set of squares and a strip with bounded width and infinite height, we consider a square strip packaging problem, which we call the square independent packing problem (SIPP), to minimize the strip height so that all the squares are packed into independent cells separated by horizontal and vertical partitions. For the SIPP, we first investigate efficient solution representations and propose a compact representation that reduces the search space from <span><math><mi>Ω</mi><mo>(</mo><mi>n</mi><mo>!</mo><mo>)</mo></math></span> to <span><math><mi>O</mi><mo>(</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span>, with <em>n</em> the number of given squares, while guaranteeing that there exists a solution representation that corresponds to an optimal solution. Based on the solution representation, we show that the problem is <span><math><mi>NP</mi></math></span>-hard. To solve the SIPP, we propose a dynamic programming method that can be extended to a fully polynomial-time approximation scheme (FPTAS). We also propose three mathematical programming formulations based on different solution representations and confirm their performance through computational experiments with a mathematical programming solver. Finally, we discuss several extensions that are relevant to practical applications.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1024 ","pages":"Article 114910"},"PeriodicalIF":0.9,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-15DOI: 10.1016/j.tcs.2024.114902
Christian Cachin, David Lehnherr, Thomas Studer
Simplicial complexes are a successful model for distributed computing. They have recently been observed to provide an interesting model for epistemic multi-agent logic where the agents' local states are the main building blocks (instead of the global states). A natural generalization is to study epistemic logic on semi-simplicial sets. However, finding the appropriate modal logic for semi-simplicial models has been an open question. We answer this by introducing the logic of synergistic knowledge and establishing its soundness and completeness.
{"title":"Synergistic knowledge","authors":"Christian Cachin, David Lehnherr, Thomas Studer","doi":"10.1016/j.tcs.2024.114902","DOIUrl":"10.1016/j.tcs.2024.114902","url":null,"abstract":"<div><div>Simplicial complexes are a successful model for distributed computing. They have recently been observed to provide an interesting model for epistemic multi-agent logic where the agents' local states are the main building blocks (instead of the global states). A natural generalization is to study epistemic logic on semi-simplicial sets. However, finding the appropriate modal logic for semi-simplicial models has been an open question. We answer this by introducing the logic of synergistic knowledge and establishing its soundness and completeness.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1023 ","pages":"Article 114902"},"PeriodicalIF":0.9,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142446330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-11DOI: 10.1016/j.tcs.2024.114904
Shunhao Oh , Dana Randall , Andréa W. Richa
We develop a framework for self-induced phase changes in programmable matter in which a collection of agents with limited computational and communication capabilities can collectively perform appropriate global tasks in response to local stimuli that dynamically appear and disappear. Agents are represented by vertices in a dynamic graph whose edge set changes over time, and stimuli are placed adversarially on the vertices of where each agent is only capable of recognizing a co-located stimulus. Agents communicate via token passing along edges to alert other agents to transition to an Aware state when stimuli are present and an Unaware state when the stimuli disappear. We present an Adaptive Stimuli Algorithm that can handle arbitrary adversarial stimulus dynamics, while an adversary (or the agents themselves) reconfigures the connections (edges) of over time in a controlled way. This algorithm can be used to solve the foraging problem on reconfigurable graphs where, in addition to food sources (stimuli) being discovered, removed, or shifted arbitrarily, we would like the agents to consistently self-organize, using only local interactions, such that if the food remains in a position long enough, the agents transition to a gather phase in which many collectively form a single large component with small perimeter around the food. Alternatively, if no food source has existed recently, the agents should undergo a self-induced collective phase change and switch to a search phase in which they distribute themselves randomly throughout the graph to search for food. Unlike previous approaches to foraging, this process is indefinitely repeatable, withstanding competing broadcast waves of state transition that may interfere with each other. Like a physical phase change, such as the ferromagnetic models underlying the gather and search algorithms used for foraging, microscopic changes in the environment trigger these macroscopic, system-wide transitions as agents share information and respond locally to get the desired collective response.
我们为可编程物质中的自诱导相变开发了一个框架，在这个框架中，具有有限计算和通信能力的代理集合可以针对动态出现和消失的局部刺激，集体执行适当的全局任务。代理由动态图 G 中的顶点表示，G 的边集随着时间的推移而变化，刺激物以对抗方式放置在 G 的顶点上，每个代理只能识别一个同位置的刺激物。各代理通过沿边传递标记的方式进行通信，以提醒其他代理在刺激出现时过渡到 "感知 "状态，在刺激消失时过渡到 "不感知 "状态。我们提出了一种自适应刺激算法，它可以处理任意对抗性刺激动态，而对抗者（或代理本身）会随着时间的推移以可控的方式重新配置 G 的连接（边）。这种算法可用于解决可重构图上的觅食问题，在这种情况下，除了食物源（刺激物）会被发现、移除或任意移动外，我们还希望代理能够持续地进行自组织，只使用局部交互作用，这样，如果食物在某个位置停留的时间足够长，代理就会过渡到聚集阶段，在这个阶段，许多代理会共同形成一个单一的大分量，食物周围的分量较小。另一种情况是，如果最近没有食物来源，觅食者就会发生由自身引起的集体相变，转入搜索阶段，在整个图中随机分布，寻找食物。与以往的觅食方法不同，这一过程可无限期重复，并能抵御可能相互干扰的状态转换广播波。就像物理相变一样，例如用于觅食的聚集和搜索算法所依据的铁磁模型，环境中的微观变化会触发这些宏观的、全系统范围的转换，因为代理会共享信息并作出局部反应，以获得所需的集体响应。
{"title":"Adaptive collective responses to local stimuli in anonymous dynamic networks","authors":"Shunhao Oh , Dana Randall , Andréa W. Richa","doi":"10.1016/j.tcs.2024.114904","DOIUrl":"10.1016/j.tcs.2024.114904","url":null,"abstract":"<div><div>We develop a framework for self-induced phase changes in programmable matter in which a collection of agents with limited computational and communication capabilities can collectively perform appropriate global tasks in response to local stimuli that dynamically appear and disappear. Agents are represented by vertices in a dynamic graph <span><math><mi>G</mi></math></span> whose edge set changes over time, and stimuli are placed adversarially on the vertices of <span><math><mi>G</mi></math></span> where each agent is only capable of recognizing a co-located stimulus. Agents communicate via token passing along edges to alert other agents to transition to an <span>Aware</span> state when stimuli are present and an <span>Unaware</span> state when the stimuli disappear. We present an Adaptive Stimuli Algorithm that can handle arbitrary adversarial stimulus dynamics, while an adversary (or the agents themselves) reconfigures the connections (edges) of <span><math><mi>G</mi></math></span> over time in a controlled way. This algorithm can be used to solve the <em>foraging problem</em> on reconfigurable graphs where, in addition to food sources (stimuli) being discovered, removed, or shifted arbitrarily, we would like the agents to consistently self-organize, using only local interactions, such that if the food remains in a position long enough, the agents transition to a <em>gather phase</em> in which many collectively form a single large component with small perimeter around the food. Alternatively, if no food source has existed recently, the agents should undergo a self-induced collective phase change and switch to a <em>search phase</em> in which they distribute themselves randomly throughout the graph to search for food. Unlike previous approaches to foraging, this process is indefinitely repeatable, withstanding competing broadcast waves of state transition that may interfere with each other. Like a physical phase change, such as the ferromagnetic models underlying the gather and search algorithms used for foraging, microscopic changes in the environment trigger these macroscopic, system-wide transitions as agents share information and respond locally to get the desired collective response.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1024 ","pages":"Article 114904"},"PeriodicalIF":0.9,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-10DOI: 10.1016/j.tcs.2024.114897
Yifei Li, Ruixi Huang, Hao Ye, Hejiao Huang, Hongwei Du
Recently, the Multi-Agent Pickup and Delivery (MAPD) problem has attracted widespread attention from both academia and industry. In the MAPD problem, each task has its pickup and delivery locations, and the agent needs to pick this task up from the pickup location and deliver it to its delivery location. Therefore, existing works consider the MAPD problem as the core problem in industrial scenarios, e.g., logistics warehouse. Note that the agents considered in the MAPD problem are single-load agents that complete tasks one by one. However, many commercial companies have deployed agents with multi-load instead of single-load agents to improve efficiency and reduce costs. The agents with multi-load can complete multiple tasks at once, so existing solutions cannot work well with the MAPD problem for multi-agents. To solve this issue, we investigate a novel problem in this paper, namely the Multi-Load Agent Pickup and Delivery (MLAPD) problem, where the agents with multi-load not only need to complete assigned real-time tasks but also need to avoid conflicts with each other and the goal is to minimize the total cost in the warehouse. To address this novel problem, we develop a task assignment to complete the assignments between multi-load agents and online tasks in real-time and a dynamic path finding problem that enables multi-load agents to move along conflict-free paths. Finally, extensive experiments in two different warehouses examine the effectiveness of our solutions.
{"title":"Dynamic path finding for multi-load agent pickup and delivery problem","authors":"Yifei Li, Ruixi Huang, Hao Ye, Hejiao Huang, Hongwei Du","doi":"10.1016/j.tcs.2024.114897","DOIUrl":"10.1016/j.tcs.2024.114897","url":null,"abstract":"<div><div>Recently, the Multi-Agent Pickup and Delivery (MAPD) problem has attracted widespread attention from both academia and industry. In the MAPD problem, each task has its pickup and delivery locations, and the agent needs to pick this task up from the pickup location and deliver it to its delivery location. Therefore, existing works consider the MAPD problem as the core problem in industrial scenarios, e.g., logistics warehouse. Note that the agents considered in the MAPD problem are single-load agents that complete tasks one by one. However, many commercial companies have deployed agents with multi-load instead of single-load agents to improve efficiency and reduce costs. The agents with multi-load can complete multiple tasks at once, so existing solutions cannot work well with the MAPD problem for multi-agents. To solve this issue, we investigate a novel problem in this paper, namely the Multi-Load Agent Pickup and Delivery (MLAPD) problem, where the agents with multi-load not only need to complete assigned real-time tasks but also need to avoid conflicts with each other and the goal is to minimize the total cost in the warehouse. To address this novel problem, we develop a task assignment to complete the assignments between multi-load agents and online tasks in real-time and a dynamic path finding problem that enables multi-load agents to move along conflict-free paths. Finally, extensive experiments in two different warehouses examine the effectiveness of our solutions.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1023 ","pages":"Article 114897"},"PeriodicalIF":0.9,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-10DOI: 10.1016/j.tcs.2024.114901
Kaiqi Zhang , Siyuan Zhang , Jirun Gao , Hongzhi Wang , Hong Gao , Jianzhong Li
<div><div>We first study maximum containing circle problem. The input to the problem is a weighted set of points and a circle of fixed radius, and the output is a suitable location of the circle such that the sum of the weights of the points covered by the circle is maximized. We propose a special polygon, called symmetrical rectilinear polygon (SRP). In this paper, we give a method for constructing the circumscribed SRP of a circle and prove the area relationship between this polygon and the circle. We solve the maximum containing SRP problem exactly, and based on this, give an algorithm for solving the <span><math><mo>(</mo><mn>1</mn><mo>−</mo><mi>ε</mi><mo>)</mo></math></span>-approximation of maximum containing circle problem. We also show that the algorithm is valid for most inputs. It only needs <span><math><mi>O</mi><mrow><mo>(</mo><mi>n</mi><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mrow><mi>log</mi></mrow><mspace></mspace><mi>n</mi><mo>+</mo><mi>n</mi><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mi>log</mi><mo></mo><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>ε</mi></mrow></mfrac><mo>)</mo></mrow><mo>)</mo></mrow></math></span> time for unit points and <span><math><mi>o</mi><mrow><mo>(</mo><mi>n</mi><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><mspace></mspace><mrow><mi>log</mi></mrow><mspace></mspace><mi>n</mi><mo>)</mo></mrow></math></span> time for weighted points. Due to its low time complexity, the algorithm can run as a stand-alone algorithm or as a preprocessor for other algorithms. As an extension of our work, we discuss a 3D version of the unweighted maximum containing circle problem, i.e., containing the maximum number of points with a given sphere. We give a <span><math><mo>(</mo><mn>1</mn><mo>−</mo><mi>ε</mi><mo>)</mo></math></span>-approximation algorithm for this problem that returns correct results in <span><math><mi>m</mi><mi>a</mi><mi>x</mi><mo>{</mo><mi>O</mi><mrow><mo>(</mo><mrow><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup><mo>/</mo><msup><mrow><mi>log</mi></mrow><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mo></mo><mo>(</mo><mi>n</mi><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo>)</mo><mo>)</mo></mrow><msup><mrow><mo>(</mo><mi>log</mi><mo></mo><mi>log</mi><mo></mo><mo>(</mo><mi>n</mi><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo>)</mo><mo>)</mo></mrow><mrow><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>)</mo></mrow><mo>,</mo><mi>o</mi><mrow><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mo>(</mo><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mrow><mi>log</mi></mrow><mspace></mspace><mi>n</mi><mo>)</mo></mrow><mrow><mn>2</mn></mr
{"title":"Approximation algorithms for finding maximum containing circle and sphere","authors":"Kaiqi Zhang , Siyuan Zhang , Jirun Gao , Hongzhi Wang , Hong Gao , Jianzhong Li","doi":"10.1016/j.tcs.2024.114901","DOIUrl":"10.1016/j.tcs.2024.114901","url":null,"abstract":"<div><div>We first study maximum containing circle problem. The input to the problem is a weighted set of points and a circle of fixed radius, and the output is a suitable location of the circle such that the sum of the weights of the points covered by the circle is maximized. We propose a special polygon, called symmetrical rectilinear polygon (SRP). In this paper, we give a method for constructing the circumscribed SRP of a circle and prove the area relationship between this polygon and the circle. We solve the maximum containing SRP problem exactly, and based on this, give an algorithm for solving the <span><math><mo>(</mo><mn>1</mn><mo>−</mo><mi>ε</mi><mo>)</mo></math></span>-approximation of maximum containing circle problem. We also show that the algorithm is valid for most inputs. It only needs <span><math><mi>O</mi><mrow><mo>(</mo><mi>n</mi><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mrow><mi>log</mi></mrow><mspace></mspace><mi>n</mi><mo>+</mo><mi>n</mi><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mi>log</mi><mo></mo><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>ε</mi></mrow></mfrac><mo>)</mo></mrow><mo>)</mo></mrow></math></span> time for unit points and <span><math><mi>o</mi><mrow><mo>(</mo><mi>n</mi><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><mspace></mspace><mrow><mi>log</mi></mrow><mspace></mspace><mi>n</mi><mo>)</mo></mrow></math></span> time for weighted points. Due to its low time complexity, the algorithm can run as a stand-alone algorithm or as a preprocessor for other algorithms. As an extension of our work, we discuss a 3D version of the unweighted maximum containing circle problem, i.e., containing the maximum number of points with a given sphere. We give a <span><math><mo>(</mo><mn>1</mn><mo>−</mo><mi>ε</mi><mo>)</mo></math></span>-approximation algorithm for this problem that returns correct results in <span><math><mi>m</mi><mi>a</mi><mi>x</mi><mo>{</mo><mi>O</mi><mrow><mo>(</mo><mrow><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup><mo>/</mo><msup><mrow><mi>log</mi></mrow><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mo></mo><mo>(</mo><mi>n</mi><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo>)</mo><mo>)</mo></mrow><msup><mrow><mo>(</mo><mi>log</mi><mo></mo><mi>log</mi><mo></mo><mo>(</mo><mi>n</mi><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo>)</mo><mo>)</mo></mrow><mrow><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>)</mo></mrow><mo>,</mo><mi>o</mi><mrow><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mo>(</mo><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mrow><mi>log</mi></mrow><mspace></mspace><mi>n</mi><mo>)</mo></mrow><mrow><mn>2</mn></mr","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1023 ","pages":"Article 114901"},"PeriodicalIF":0.9,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142434050","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-10DOI: 10.1016/j.tcs.2024.114898
Jianming Zhu , Ye Xing , Runzhi Li , Smita Ghosh , Priyanshi Garg , Weili Wu
Rumor sources spread negative information throughout the network, which may cause unbelievable results in real society especially for social safety field. Propagating positive information from several “protector” users is an effective method for rumor blocking once the rumor is detected. Based on the probability of each user being a rumor, “protector” nodes need to be selected in order to prepare for rumor blocking. Given a social network , where is the probability that v is activated by u after u is activated, and Q is the weight function on node set V, is the probability that v will be a rumor source. Stochastic Rumor Blocking (SRB) problem is to select k nodes as “protector” such that the expected eventually influenced users by rumor is minimized. SRB will be proved to be NP-hard and the objective function is supermodular. We present a Compound Reverse Influence Set sampling method for estimation of the objective value which can be represented as a compound set function. A randomized greedy algorithm with theoretical analysis will be presented and other two different “protector” selection strategies will be proposed for comparison. Finally, we evaluate our algorithm on real world data sets and do comparison among different strategies.
谣言源会在整个网络中传播负面信息，这可能会在现实社会中造成令人难以置信的结果，尤其是在社会安全领域。一旦发现谣言，由多个 "保护者 "用户传播正面信息是一种有效的谣言阻断方法。根据每个用户成为谣言的概率，需要选择 "保护者 "节点，为谣言阻断做准备。给定一个社交网络 G=（V,E,P,Q），其中 P(u,v) 是 u 激活后 v 被 u 激活的概率，Q 是节点集 V 的权重函数，Qv 是 v 成为谣言源的概率。随机谣言阻断（SRB）问题是选择 k 个节点作为 "保护者"，使最终受谣言影响的用户数量最小。SRB 将被证明是 NP 难问题，而且目标函数是超模的。我们提出了一种用于估计目标值的复合反向影响集抽样方法，该方法可以表示为一个复合集函数。此外，我们还将介绍一种带有理论分析的随机贪婪算法，并提出其他两种不同的 "保护者 "选择策略进行比较。最后，我们将在实际数据集上评估我们的算法，并对不同的策略进行比较。
{"title":"Efficient algorithm for stochastic rumor blocking problem in social networks during safety accident period","authors":"Jianming Zhu , Ye Xing , Runzhi Li , Smita Ghosh , Priyanshi Garg , Weili Wu","doi":"10.1016/j.tcs.2024.114898","DOIUrl":"10.1016/j.tcs.2024.114898","url":null,"abstract":"<div><div>Rumor sources spread negative information throughout the network, which may cause unbelievable results in real society especially for social safety field. Propagating positive information from several “protector” users is an effective method for rumor blocking once the rumor is detected. Based on the probability of each user being a rumor, “protector” nodes need to be selected in order to prepare for rumor blocking. Given a social network <span><math><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>,</mo><mi>P</mi><mo>,</mo><mi>Q</mi><mo>)</mo></math></span>, where <span><math><msub><mrow><mi>P</mi></mrow><mrow><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow></msub></math></span> is the probability that <em>v</em> is activated by <em>u</em> after <em>u</em> is activated, and <em>Q</em> is the weight function on node set <em>V</em>, <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>v</mi></mrow></msub></math></span> is the probability that <em>v</em> will be a rumor source. Stochastic Rumor Blocking (SRB) problem is to select <em>k</em> nodes as “protector” such that the expected eventually influenced users by rumor is minimized. SRB will be proved to be NP-hard and the objective function is supermodular. We present a Compound Reverse Influence Set sampling method for estimation of the objective value which can be represented as a compound set function. A randomized greedy algorithm with theoretical analysis will be presented and other two different “protector” selection strategies will be proposed for comparison. Finally, we evaluate our algorithm on real world data sets and do comparison among different strategies.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1023 ","pages":"Article 114898"},"PeriodicalIF":0.9,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142434048","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-09DOI: 10.1016/j.tcs.2024.114899
Julio Aracena , Luis Cabrera-Crot , Adrien Richard , Lilian Salinas
The study of the dynamical behavior of Boolean networks with different update schedules has so far focused primarily on the possible dynamics and equivalent networks that can be obtained. However, few studies have been done about which networks can be obtained from another network with a non-parallel schedule.
In this article, we define the problem of finding a Boolean network that is dynamically equivalent to another network. For the general case, it is shown that the problem is NP-Hard. However, if the problem is restricted to disjunctive Boolean networks, it can be solved in polynomial time.
{"title":"Dynamically equivalent disjunctive networks","authors":"Julio Aracena , Luis Cabrera-Crot , Adrien Richard , Lilian Salinas","doi":"10.1016/j.tcs.2024.114899","DOIUrl":"10.1016/j.tcs.2024.114899","url":null,"abstract":"<div><div>The study of the dynamical behavior of Boolean networks with different update schedules has so far focused primarily on the possible dynamics and equivalent networks that can be obtained. However, few studies have been done about which networks can be obtained from another network with a non-parallel schedule.</div><div>In this article, we define the problem of finding a Boolean network that is dynamically equivalent to another network. For the general case, it is shown that the problem is NP-Hard. However, if the problem is restricted to disjunctive Boolean networks, it can be solved in polynomial time.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1024 ","pages":"Article 114899"},"PeriodicalIF":0.9,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535254","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-09DOI: 10.1016/j.tcs.2024.114896
Jing Yuan , Shaojie Tang
This paper addresses the problem of creating decision trees for identifying hypotheses, also known as entities, in a setting where the cost of an action is dependent on the true hypothesis. Specifically, we consider the scenario where n hypotheses are divided into m groups based on their priority levels. Taking an action on a higher priority hypothesis incurs a higher cost. This is relevant to many real-world applications where cost-sensitive decisions need to be made. For example, in a medical diagnosis task, the goal is to take a series of actions (such as medical tests) to identify a cause. Each action in this process requires conducting a test on the patient and observing the outcome, which can take anywhere from a few minutes to several weeks depending on the test. In this case, the cost (the result of waiting for the outcome) is higher if the true hypothesis is more time-sensitive. For example, if the true hypothesis is toxic chemical exposure (as opposed to a chronic disease such as diabetes), a delay of a few minutes could significantly increase the patient's risk of mortality. We propose a group greedy algorithm to solve this problem. We demonstrate that under worst-case scenarios, our algorithm has an approximation ratio of . Importantly, when , meaning there is only one group of hypotheses, our result is consistent with the logarithmic approximation bound for the traditional optimal decision tree problem.
本文探讨了在行动成本取决于真实假设的情况下，创建决策树以识别假设（也称实体）的问题。具体来说，我们考虑了这样一种情况：n 个假设根据其优先级被分为 m 组。对优先级较高的假设采取行动会产生较高的成本。这与现实世界中许多需要做出成本敏感决策的应用相关。例如，在医疗诊断任务中，目标是采取一系列行动（如医学测试）来确定病因。这一过程中的每项行动都需要对病人进行测试并观察结果，根据测试内容的不同，测试时间从几分钟到几周不等。在这种情况下，如果真实假设对时间的敏感性更高，那么成本（等待结果的结果）就会更高。例如，如果真实假设是接触有毒化学物质（而不是糖尿病等慢性疾病），那么几分钟的延迟就会大大增加患者的死亡风险。我们提出了一种群体贪婪算法来解决这个问题。我们证明，在最坏的情况下，我们的算法的近似率为 O(mlogn)。重要的是，当 m=1 时，即只有一组假设，我们的结果与传统最优决策树问题的对数近似边界一致。
{"title":"Approximating decision trees with priority hypotheses","authors":"Jing Yuan , Shaojie Tang","doi":"10.1016/j.tcs.2024.114896","DOIUrl":"10.1016/j.tcs.2024.114896","url":null,"abstract":"<div><div>This paper addresses the problem of creating decision trees for identifying hypotheses, also known as entities, in a setting where the cost of an action is dependent on the true hypothesis. Specifically, we consider the scenario where <em>n</em> hypotheses are divided into <em>m</em> groups based on their priority levels. Taking an action on a higher priority hypothesis incurs a higher cost. This is relevant to many real-world applications where cost-sensitive decisions need to be made. For example, in a medical diagnosis task, the goal is to take a series of actions (such as medical tests) to identify a cause. Each action in this process requires conducting a test on the patient and observing the outcome, which can take anywhere from a few minutes to several weeks depending on the test. In this case, the cost (the result of waiting for the outcome) is higher if the true hypothesis is more time-sensitive. For example, if the true hypothesis is toxic chemical exposure (as opposed to a chronic disease such as diabetes), a delay of a few minutes could significantly increase the patient's risk of mortality. We propose a group greedy algorithm to solve this problem. We demonstrate that under worst-case scenarios, our algorithm has an approximation ratio of <span><math><mi>O</mi><mo>(</mo><mi>m</mi><mi>log</mi><mo></mo><mi>n</mi><mo>)</mo></math></span>. Importantly, when <span><math><mi>m</mi><mo>=</mo><mn>1</mn></math></span>, meaning there is only one group of hypotheses, our result is consistent with the logarithmic approximation bound for the traditional optimal decision tree problem.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1023 ","pages":"Article 114896"},"PeriodicalIF":0.9,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142434047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-09DOI: 10.1016/j.tcs.2024.114900
Andrew Bloch-Hansen , Roberto Solis-Oba , Daniel R. Page
We consider the scenario of routing an agent called a thief through a weighted graph from a start vertex s to an end vertex t. A set I of items each with weight and profit is distributed among . The thief, who has a knapsack of capacity W, must follow a simple path from s to t within a given time T while packing in the knapsack a set of items taken from the vertices along the path of total weight at most W and maximum profit. The travel time across an edge depends on the edge length and current knapsack load.
The thief orienteering problem (ThOP) is a generalization of the orienteering problem, the longest path problem, and the 0-1 knapsack problem. We prove that there exists no approximation algorithm for ThOP with constant approximation ratio unless , and we present a polynomial-time approximation scheme (PTAS) for a relaxed version of ThOP when G is directed and acyclic that produces solutions that use time at most for any constant . We also present a fully polynomial-time approximation scheme (FPTAS) for ThOP on arbitrary undirected graphs where the travel time depends only on the lengths of the edges and T is the length of a shortest path from s to t plus a constant K. Finally, we present a FPTAS for a restricted version of the problem where the input graph is a clique.
我们考虑的情况是，让一个名为 "小偷 "的代理通过加权图 G=(V,E) 从起点顶点 s 到终点顶点 t。小偷有一个容量为 W 的背包，他必须在给定的时间 T 内沿着一条简单的路径从 s 到 t，同时在背包中装入一组从沿路顶点取来的物品，这些物品的总重量最多为 W，利润最大。小偷定向问题（ThOP）是定向问题、最长路径问题和 0-1 包问题的一般化。我们证明了除非 P=NP 否则不存在近似率恒定的 ThOP 近似算法，并针对 G 为有向、无环的松弛版 ThOP 提出了多项式时间近似方案 (PTAS)，对于任意常数ϵ>0，该方案产生的解最多耗时 T(1+ϵ)。我们还为任意无向图上的 ThOP 提出了一种全多项式时间近似方案 (FPTAS)，在这种近似方案中，旅行时间只取决于边的长度，T 是 s 到 t 的最短路径长度加上常数 K。
{"title":"Algorithms for the thief orienteering problem on directed acyclic graphs","authors":"Andrew Bloch-Hansen , Roberto Solis-Oba , Daniel R. Page","doi":"10.1016/j.tcs.2024.114900","DOIUrl":"10.1016/j.tcs.2024.114900","url":null,"abstract":"<div><div>We consider the scenario of routing an agent called a <em>thief</em> through a weighted graph <span><math><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></math></span> from a start vertex <em>s</em> to an end vertex <em>t</em>. A set <em>I</em> of items each with weight <span><math><msub><mrow><mi>w</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> and profit <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> is distributed among <span><math><mi>V</mi><mo>∖</mo><mo>{</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo>}</mo></math></span>. The thief, who has a knapsack of capacity <em>W</em>, must follow a simple path from <em>s</em> to <em>t</em> within a given time <em>T</em> while packing in the knapsack a set of items taken from the vertices along the path of total weight at most <em>W</em> and maximum profit. The travel time across an edge depends on the edge length and current knapsack load.</div><div>The thief orienteering problem (ThOP) is a generalization of the orienteering problem, the longest path problem, and the 0-1 knapsack problem. We prove that there exists no approximation algorithm for ThOP with constant approximation ratio unless <span><math><mtext>P</mtext><mo>=</mo><mtext>NP</mtext></math></span>, and we present a polynomial-time approximation scheme (PTAS) for a relaxed version of ThOP when <em>G</em> is directed and acyclic that produces solutions that use time at most <span><math><mi>T</mi><mo>(</mo><mn>1</mn><mo>+</mo><mi>ϵ</mi><mo>)</mo></math></span> for any constant <span><math><mi>ϵ</mi><mo>></mo><mn>0</mn></math></span>. We also present a fully polynomial-time approximation scheme (FPTAS) for ThOP on arbitrary undirected graphs where the travel time depends only on the lengths of the edges and <em>T</em> is the length of a shortest path from <em>s</em> to <em>t</em> plus a constant <em>K</em>. Finally, we present a FPTAS for a restricted version of the problem where the input graph is a clique.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1023 ","pages":"Article 114900"},"PeriodicalIF":0.9,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142427852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-04DOI: 10.1016/j.tcs.2024.114895
Jie Zhao , Hejiao Huang , Yongliang Xu , Xiaojun Zhang , Hongwei Du , Chao Huang
Cloud-assisted e-healthcare sharing systems (EHSSs) play an increasingly pivotal role in the contemporary healthcare field. By outsourcing electronic medical records (EMRs) to the cloud, hospitals can alleviate local storage and management burdens while facilitating data sharing. Due to the highly sensitive nature of EMRs, encryption is necessary before storing them on the cloud. Attribute-based keyword search (ABKS) enables the privacy protection of EMRs with efficient search services. However, there remain some limitations in practical application. Firstly, most ABKS schemes only support single keyword queries, resulting in inaccurate results and wastage of computing and bandwidth resources. Secondly, since sensitive information within EMRs is encrypted as a whole, different data users (including internal doctors and external researchers) should have varying access rights to prevent leakage of this sensitive information. Thirdly, incorrect search results could lead to misdiagnosis or endanger patients' lives and affect researchers' decision-making processes. To effectively tackle these challenges, this paper proposes a verifiable attribute-based multi-keyword search scheme with sensitive information hiding (VABMKS-SIH) for cloud-assisted EHSSs, where we present a secure model for multi-keyword search with two-level access structure by incorporating an improved blindness filtering technique into ciphertext-policy attribute-based encryption (CP-ABE) within existing keyword search framework. Our scheme employs a super-increasing sequence to aggregate multiple filtered data blocks into one unified ciphertext, thereby greatly reducing communication overhead during the transmission phases of ciphertext. To check the correctness of returned results, we introduce a lightweight algebraic signature algorithm based on fundamental algebraic operations. A security analysis demonstrates that VABMKS-SIH is provably secure under the random oracle mode. Additionally, we also evaluate the proposed scheme's performance to demonstrate its utility in cloud-assisted EHSSs.
{"title":"Verifiable attribute-based multi-keyword search scheme with sensitive information hiding for cloud-assisted e-healthcare sharing systems","authors":"Jie Zhao , Hejiao Huang , Yongliang Xu , Xiaojun Zhang , Hongwei Du , Chao Huang","doi":"10.1016/j.tcs.2024.114895","DOIUrl":"10.1016/j.tcs.2024.114895","url":null,"abstract":"<div><div>Cloud-assisted e-healthcare sharing systems (EHSSs) play an increasingly pivotal role in the contemporary healthcare field. By outsourcing electronic medical records (EMRs) to the cloud, hospitals can alleviate local storage and management burdens while facilitating data sharing. Due to the highly sensitive nature of EMRs, encryption is necessary before storing them on the cloud. Attribute-based keyword search (ABKS) enables the privacy protection of EMRs with efficient search services. However, there remain some limitations in practical application. Firstly, most ABKS schemes only support single keyword queries, resulting in inaccurate results and wastage of computing and bandwidth resources. Secondly, since sensitive information within EMRs is encrypted as a whole, different data users (including internal doctors and external researchers) should have varying access rights to prevent leakage of this sensitive information. Thirdly, incorrect search results could lead to misdiagnosis or endanger patients' lives and affect researchers' decision-making processes. To effectively tackle these challenges, this paper proposes a verifiable attribute-based multi-keyword search scheme with sensitive information hiding (VABMKS-SIH) for cloud-assisted EHSSs, where we present a secure model for multi-keyword search with two-level access structure by incorporating an improved blindness filtering technique into ciphertext-policy attribute-based encryption (CP-ABE) within existing keyword search framework. Our scheme employs a super-increasing sequence to aggregate multiple filtered data blocks into one unified ciphertext, thereby greatly reducing communication overhead during the transmission phases of ciphertext. To check the correctness of returned results, we introduce a lightweight algebraic signature algorithm based on fundamental algebraic operations. A security analysis demonstrates that VABMKS-SIH is provably secure under the random oracle mode. Additionally, we also evaluate the proposed scheme's performance to demonstrate its utility in cloud-assisted EHSSs.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1023 ","pages":"Article 114895"},"PeriodicalIF":0.9,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142427853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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