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Faster algorithms for evacuation problems in networks with a single sink of small degree and bounded capacitated edges 具有小度单汇和有界容纳边的网络中疏散问题的更快算法
IF 1 4区 数学 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-10-07 DOI: 10.1007/s10878-024-01213-y
Yuya Higashikawa, Naoki Katoh, Junichi Teruyama, Yuki Tokuni

In this paper, we propose new algorithms for evacuation problems defined on dynamic flow networks. A dynamic flow network is a directed graph in which source nodes are given supplies and a single sink node is given a demand. The evacuation problem seeks a dynamic flow that sends all supplies from sources to the sink such that its demand is satisfied in the minimum feasible time horizon. For this problem, the current best algorithms are developed by Schlöter (2018) and Kamiyama (2019), which run in strongly polynomial time but with high-order polynomial time complexity because they use submodular function minimization as a subroutine. In this paper, we propose new algorithms that do not explicitly execute submodular function minimization, and we prove that they are faster than the current best algorithms when an input network is restricted such that the sink has a small in-degree and every edge has the same capacity.

在本文中,我们针对动态流动网络上定义的疏散问题提出了新的算法。动态流动网络是一个有向图,其中源节点给出供应,单个汇节点给出需求。疏散问题寻求的是一种动态流,它能将所有供应从源节点发送到汇节点,从而在最小可行时间范围内满足其需求。对于这个问题,目前最好的算法是由 Schlöter (2018) 和 Kamiyama (2019) 开发的,其运行时间为强多项式时间,但具有高阶多项式时间复杂度,因为它们使用了子模函数最小化作为子程序。在本文中,我们提出了不显式执行子模函数最小化的新算法,并证明当输入网络受到限制,使得汇的内度很小且每条边的容量相同时,这些算法比目前最好的算法更快。
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引用次数: 0
The k-th Roman domination problem is polynomial on interval graphs 第 k 个罗马支配问题在区间图上是多项式问题
IF 1 4区 数学 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-10-05 DOI: 10.1007/s10878-024-01206-x
Peng Li

Let G be some simple graph and k be any positive integer. Take (h: V(G)rightarrow {0,1,ldots ,k+1}) and (v in V(G)), let (AN_{h}(v)) denote the set of vertices (win N_{G}(v)) with (h(w)ge 1). Let (AN_{h}[v] = AN_{h}(v)cup {v}). The function h is a [k]-Roman dominating function of G if (h(AN_{h}[v]) ge |AN_{h}(v)| + k) holds for any (v in V(G)). The minimum weight of such a function is called the k-th Roman Domination number of G, which is denoted by (gamma _{kR}(G)). In 2020, Banerjee et al. presented linear time algorithms to compute the double Roman domination number on proper interval graphs and block graphs. They posed the open question that whether there is some polynomial time algorithm to solve the double Roman domination problem on interval graphs. It is argued that the interval graph is a nontrivial graph class. In this article, we design a simple dynamic polynomial time algorithm to solve the k-th Roman domination problem on interval graphs for each fixed integer (k>1).

让 G 是某个简单图形,k 是任意正整数。取(h:V(G)rightarrow {0,1,ldots ,k+1}) 和 (v in V(G)), let (AN_{h}(v)) denote the set of vertices (win N_{G}(v)) with (h(w)ge 1).让(AN_{h}[v] = AN_{h}(v)cup {v})。函数 h 是 G 的 [k]-Roman 主导函数,如果对于任意 (v in V(G)) (h(AN_{h}[v]) ge |AN_{h}(v)| + k) 成立。这样一个函数的最小权重被称为 G 的第 k 个罗马支配数,用 (gamma _{kR}(G)) 表示。2020 年,Banerjee 等人提出了在适当区间图和块图上计算双罗马支配数的线性时间算法。他们提出了一个开放性问题,即是否存在某种多项式时间算法来解决区间图上的双罗马支配数问题。他们认为区间图是一个非难图类。在本文中,我们设计了一种简单的动态多项式时间算法来解决区间图上每个固定整数 (k>1)的 k-th Roman domination 问题。
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引用次数: 0
Efficient branch-and-bound algorithms for finding triangle-constrained 2-clubs 寻找三角形受限 2-club 的高效分支和约束算法
IF 1 4区 数学 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-09-21 DOI: 10.1007/s10878-024-01204-z
Niels Grüttemeier, Philipp Heinrich Keßler, Christian Komusiewicz, Frank Sommer

In the Vertex Triangle 2-Club problem, we are given an undirected graph G and aim to find a maximum-vertex subgraph of G that has diameter at most 2 and in which every vertex is contained in at least (ell ) triangles in the subgraph. So far, the only algorithm for solving Vertex Triangle 2-Club relies on an ILP formulation (Almeida and Brás in Comput Oper Res 111:258–270, 2019). In this work, we develop a combinatorial branch-and-bound algorithm that, coupled with a set of data reduction rules, outperforms the existing implementation and is able to find optimal solutions on sparse real-world graphs with more than 100,000 vertices in a few minutes. We also extend our algorithm to the Edge Triangle 2-Club problem where the triangle constraint is imposed on all edges of the subgraph.

在顶点三角形 2-Club 问题中,我们给定了一个无向图 G,目的是找到 G 的最大顶点子图,该子图的直径最多为 2,其中每个顶点至少包含在子图中的(ell )个三角形中。迄今为止,解决顶点三角形 2-Club 的唯一算法依赖于 ILP 表述(Almeida 和 Brás 发表于 Comput Oper Res 111:258-270, 2019)。在这项工作中,我们开发了一种组合式分支与边界算法,该算法与一组数据缩减规则相结合,性能优于现有实现,能够在几分钟内找到具有 10 万多个顶点的稀疏真实世界图的最优解。我们还将算法扩展到边缘三角形 2-Club 问题,在该问题中,子图的所有边缘都施加了三角形约束。
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引用次数: 0
Minmax regret 1-sink location problems on dynamic flow path networks with parametric weights 带参数权重的动态流路网络上的最小遗憾 1 汇定位问题
IF 1 4区 数学 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-08-26 DOI: 10.1007/s10878-024-01199-7
Tetsuya Fujie, Yuya Higashikawa, Naoki Katoh, Junichi Teruyama, Yuki Tokuni

This paper addresses the minmax regret 1-sink location problem on a dynamic flow path network with parametric weights. A dynamic flow path network consists of an undirected path with positive edge lengths, positive edge capacities, and nonnegative vertex weights. A path can be considered as a road, an edge length as the distance along the road, and a vertex weight as the number of people at the site. An edge capacity limits the number of people that can enter the edge per unit time. We consider the problem of locating a sink where all the people evacuate quickly. In our model, each weight is represented by a linear function of a common parameter t, and the decision maker who determines the sink location does not know the value of t. We formulate the problem under such uncertainty as the minmax regret problem. Given t and sink location x, the cost is the sum of arrival times at x for all the people determined by t. The regret for x under t is the gap between this cost and the optimal cost under t. The problem is to find the sink location minimizing the maximum regret over all t. For the problem, we propose an (O(n^4 2^{alpha (n)} alpha (n)^2 log n)) time algorithm, where n is the number of vertices in the network and (alpha (cdot )) is the inverse Ackermann function. Also, for the special case in which every edge has the same capacity, we show that the complexity can be reduced to (O(n^3 2^{alpha (n)} alpha (n) log n)).

本文解决的是具有参数权重的动态流动路径网络上的最小遗憾单汇定位问题。动态流动路径网络由具有正边长、正边容量和非负顶点权重的无向路径组成。路径可视为一条道路,边长可视为沿路的距离,顶点权重可视为该地点的人数。边的容量限制了单位时间内能进入边的人数。我们考虑的问题是找到一个汇集点,让所有的人都能快速撤离。在我们的模型中,每个权重都由一个共同参数 t 的线性函数来表示,而决定水槽位置的决策者并不知道 t 的值。给定 t 和水槽位置 x,成本是由 t 决定的所有人员到达 x 的时间之和。x 在 t 条件下的遗憾是该成本与 t 条件下最优成本之间的差距。对于这个问题,我们提出了一种耗时(O(n^4 2^{alpha (n)} alpha (n)^2 log n)的算法,其中 n 是网络中的顶点数,(alpha (cdot ))是反阿克曼函数。另外,对于每条边都有相同容量的特殊情况,我们证明复杂度可以降低到 (O(n^3 2^{alpha (n)} alpha (n) log n))。
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引用次数: 0
Efficient estimation of the modified Gromov–Hausdorff distance between unweighted graphs 非加权图之间修正的格罗莫夫-豪斯多夫距离的有效估算
IF 1 4区 数学 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-08-23 DOI: 10.1007/s10878-024-01202-1
Vladyslav Oles, Nathan Lemons, Alexander Panchenko

Gromov–Hausdorff distances measure shape difference between the objects representable as compact metric spaces, e.g. point clouds, manifolds, or graphs. Computing any Gromov–Hausdorff distance is equivalent to solving an NP-hard optimization problem, deeming the notion impractical for applications. In this paper we propose a polynomial algorithm for estimating the so-called modified Gromov–Hausdorff (mGH) distance, a relaxation of the standard Gromov–Hausdorff (GH) distance with similar topological properties. We implement the algorithm for the case of compact metric spaces induced by unweighted graphs as part of Python library scikit-tda, and demonstrate its performance on real-world and synthetic networks. The algorithm finds the mGH distances exactly on most graphs with the scale-free property. We use the computed mGH distances to successfully detect outliers in real-world social and computer networks.

格罗莫夫-豪斯多夫距离测量可表示为紧凑度量空间(如点云、流形或图形)的对象之间的形状差异。计算任何 Gromov-Hausdorff 距离都等同于解决一个 NP 难优化问题,因此这一概念在应用中并不实用。在本文中,我们提出了一种多项式算法,用于估算所谓的修正格罗莫夫-豪斯多夫(mGH)距离,它是标准格罗莫夫-豪斯多夫(GH)距离的一种松弛,具有类似的拓扑特性。作为 Python 库 scikit-tda 的一部分,我们针对无权重图引起的紧凑度量空间实现了该算法,并在真实世界和合成网络上演示了其性能。该算法能在大多数具有无标度特性的图上精确找到 mGH 距离。我们利用计算出的 mGH 距离成功地检测了现实世界社交和计算机网络中的异常值。
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引用次数: 0
Meta-heuristic-based hybrid deep learning model for vulnerability detection and prevention in software system 基于元启发式的混合深度学习模型用于软件系统的漏洞检测和预防
IF 1 4区 数学 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-08-20 DOI: 10.1007/s10878-024-01185-z
Lijin Shaji, R. Suji Pramila

Software vulnerabilities are flaws that may be exploited to cause loss or harm. Various automated machine-learning techniques have been developed in preceding studies to detect software vulnerabilities. This work tries to develop a technique for securing the software on the basis of their vulnerabilities that are already known, by developing a hybrid deep learning model to detect those vulnerabilities. Moreover, certain countermeasures are suggested based on the types of vulnerability to prevent the attack further. For different software projects taken as the dataset, feature fusion is done by utilizing canonical correlation analysis together with Deep Residual Network (DRN). A hybrid deep learning technique trained using AdamW-Rat Swarm Optimizer (AdamW-RSO) is designed to detect software vulnerability. Hybrid deep learning makes use of the Deep Belief Network (DBN) and Generative Adversarial Network (GAN). For every vulnerability, its location of occurrence within the software development procedures and techniques of alleviation via implementation level or design level activities are described. Thus, it helps in understanding the appearance of vulnerabilities, suggesting the use of various countermeasures during the initial phases of software design, and therefore, assures software security. Evaluating the performance of vulnerability detection by the proposed technique regarding recall, precision, and f-measure, it is found to be more effective than the existing methods.

软件漏洞是指可能被利用造成损失或伤害的缺陷。在之前的研究中,已经开发了各种自动化机器学习技术来检测软件漏洞。这项工作试图通过开发一种混合深度学习模型来检测这些漏洞,从而在已知漏洞的基础上开发一种确保软件安全的技术。此外,还根据漏洞类型提出了一些对策,以进一步防止攻击。对于作为数据集的不同软件项目,利用典型相关分析和深度残差网络(DRN)进行特征融合。使用 AdamW-Rat Swarm Optimizer(AdamW-RSO)训练的混合深度学习技术旨在检测软件漏洞。混合深度学习利用了深度信念网络(DBN)和生成对抗网络(GAN)。对于每个漏洞,都会描述其在软件开发程序中出现的位置,以及通过实施级或设计级活动来缓解的技术。因此,它有助于了解漏洞的出现,建议在软件设计的初始阶段使用各种对策,从而确保软件的安全性。通过评估拟议技术在召回率、精确度和 f-measure 方面的漏洞检测性能,发现它比现有方法更有效。
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引用次数: 0
The prize-collecting single machine scheduling with bounds and penalties 有约束和惩罚的单机有奖调度
IF 1 4区 数学 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-08-16 DOI: 10.1007/s10878-024-01203-0
Guojun Hu, Pengxiang Pan, Suding Liu, Ping Yang, Runtao Xie

This study investigates the prize-collecting single machine scheduling with bounds and penalties (PC-SMS-BP). In this problem, a set of n jobs and a single machine are considered, where each job (J_j) has a processing time (p_{j}), a profit (pi _{j}) and a rejection penalty (w_{j}). The upper bound on the processing number is U. The objective of this study is to find a feasible schedule that minimizes the makespan of the accepted jobs and the total rejection penalty of the rejected jobs under the condition that the number of the accepted jobs does not exceed a given threshold U while the total profit of the accepted jobs does not fall below a specified profit bound (varPi ). We first demonstrate that this problem is NP-hard. Then, a pseudo-polynomial time dynamic programming algorithm and a fully polynomial time approximation scheme (FPTAS) are proposed. Finally, numerical experiments are conducted to compare the effectiveness of the two proposed algorithms.

本研究探讨了带约束和惩罚的单机有奖调度(PC-SMS-BP)。在这个问题中,考虑了一组 n 个作业和一台单机,其中每个作业 (J_j) 有一个处理时间 (p_{j})、一个利润 (pi_{j})和一个拒绝惩罚 (w_{j})。本研究的目标是找到一个可行的时间表,在接受的作业数量不超过给定阈值 U,同时接受作业的总利润不低于指定利润阈值 (varPi )的条件下,使接受作业的工作时间和拒绝作业的总拒绝惩罚最小化。我们首先证明这个问题是 NP 难的。然后,我们提出了一种伪多项式时间动态编程算法和一种全多项式时间近似方案(FPTAS)。最后,我们通过数值实验比较了两种算法的有效性。
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引用次数: 0
On the complexity of minimum maximal acyclic matchings 论最小最大非循环匹配的复杂性
IF 1 4区 数学 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-08-07 DOI: 10.1007/s10878-024-01200-3
Juhi Chaudhary, Sounaka Mishra, B. S. Panda

Low-Acy-Matching asks to find a maximal matching M in a given graph G of minimum cardinality such that the set of M-saturated vertices induces an acyclic subgraph in G. The decision version of Low-Acy-Matching is known to be ({textsf{NP}})-complete. In this paper, we strengthen this result by proving that the decision version of Low-Acy-Matching remains ({textsf{NP}})-complete for bipartite graphs with maximum degree 6 and planar perfect elimination bipartite graphs. We also show the hardness difference between Low-Acy-Matching and Max-Acy-Matching. Furthermore, we prove that, even for bipartite graphs, Low-Acy-Matching cannot be approximated within a ratio of (n^{1-epsilon }) for any (epsilon >0) unless ({textsf{P}}={textsf{NP}}). Finally, we establish that Low-Acy-Matching exhibits (textsf{APX})-hardness when restricted to 4-regular graphs.

Low-Acy-Matching要求在给定图G中找到一个最大匹配M,该匹配M的最小卡数使得M饱和顶点集在G中诱导出一个无环子图。已知Low-Acy-Matching的决策版本是({textsf{NP}})-完全的。在本文中,我们通过证明对于最大阶数为 6 的双峰图和平面完全消元双峰图,Low-Acy-Matching 的决策版本仍然是 ({textsf{NP}}) -complete 的,从而加强了这一结果。我们还展示了 Low-Acy-Matching 和 Max-Acy-Matching 之间的难度差异。此外,我们还证明了,即使对于双峰图,对于任意 (epsilon >0),Low-Acy-Matching 也不能在 (n^{1-epsilon }) 的比率内被近似,除非 ({textsf{P}}={textsf{NP}}).最后,我们证明了当限制在 4-regular graphs 时,Low-Acy-Matching 展示了 (textsf{APX})-hardness。
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引用次数: 0
Polynomial algorithms for sparse spanners on subcubic graphs 亚立方图上稀疏跨度的多项式算法
IF 1 4区 数学 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-08-07 DOI: 10.1007/s10878-024-01197-9
R. Gómez, F. K. Miyazawa, Y. Wakababayashi

Let G be a connected graph and (t ge 1) a (rational) constant. A t-spanner of G is a spanning subgraph of G in which the distance between any pair of vertices is at most t times its distance in G. We address two problems on spanners. The first one, known as the minimum t-spanner problem (MinS (_t)), seeks in a connected graph a t-spanner with the smallest possible number of edges. In the second one, called minimum cost tree t-spanner problem (MCTS (_t)), the input graph has costs assigned to its edges and seeks a t-spanner that is a tree with minimum cost. It is an optimization version of the tree t-spanner problem (TreeS (_t)), a decision problem concerning the existence of a t-spanner that is a tree. MinS (_t) is known to be ({textsc {NP}})-hard for every (t ge 2). On the other hand, TreeS (_t) admits a polynomial-time algorithm for (t le 2) and is ({textsc {NP}})-complete for (t ge 4); but its complexity for (t=3) remains open. We focus on the class of subcubic graphs. First, we show that for such graphs MinS (_3) can be solved in polynomial time. These results yield a practical polynomial algorithm for TreeS (_3) that is of a combinatorial nature. We also show that MCTS (_2) can be solved in polynomial time. To obtain this last result, we prove a complete linear characterization of the polytope defined by the incidence vectors of the tree 2-spanners of a subcubic graph. A recent result showing that MinS (_3) on graphs with maximum degree at most 5 is NP-hard, together with the current result on subcubic graphs, leaves open only the complexity of MinS (_3) on graphs with maximum degree 4.

让 G 是一个连通图,(t)是一个(有理)常数。G 的一个 t 跨子图是 G 的一个跨子图,其中任意一对顶点之间的距离最多是它在 G 中距离的 t 倍。第一个问题被称为最小跨度问题(MinS (_t)),它在一个连通图中寻找一个边数尽可能少的跨度。第二个问题被称为最小成本树 t-spanner 问题(MCTS (_t)),输入图的边都有成本,寻求的 t-spanner 是成本最小的树。它是树 t-spanner 问题(TreeS (_t))的优化版本,是一个关于是否存在树 t-spanner 的决策问题。众所周知,MinS (_t )对于每一个 t (ge 2 )来说都是({textsc {NP}})困难的。另一方面,TreeS (_t)对于 (t le 2) 允许一个多项式时间算法,并且对于 (t ge 4) 是 ({textsc {NP}})-complete 的;但是它对于 (t=3) 的复杂性仍然是未知的。我们将重点放在亚立方图类上。首先,我们证明对于这类图,MinS (_3)可以在多项式时间内求解。这些结果为 TreeS (_3)提供了一种具有组合性质的实用多项式算法。我们还证明了 MCTS (_2)可以在多项式时间内求解。为了得到最后一个结果,我们证明了由亚立方体图的树 2-spanners 的入射向量定义的多面体的完整线性特征。最近的一个结果表明,在最大度最多为 5 的图上 MinS (_3) 是 NP 难的,加上目前关于亚立方图的结果,只剩下最大度为 4 的图上 MinS (_3) 的复杂性还没有解决。
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引用次数: 0
Approximating the probabilistic p-Center problem under pressure 逼近压力下的概率 p 中心问题
IF 1 4区 数学 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-08-07 DOI: 10.1007/s10878-024-01194-y
Marc Demange, Marcel A. Haddad, Cécile Murat

The Probabilistic p-Center problem under Pressure (Min P p CP) is a variant of the usual Min p-Center problem we recently introduced in the context of wildfire management. The problem is to locate p shelters minimizing the maximum distance people will have to cover in case of fire in order to reach the closest accessible shelter. The landscape is divided into zones and is modeled as an edge-weighted graph with vertices corresponding to zones and edges corresponding to direct connections between two adjacent zones. The risk associated with fire outbreaks is modeled using a finite set of fire scenarios. Each scenario corresponds to a fire outbreak on a single zone (i.e., on a vertex) with the main consequence of modifying evacuation paths in two ways. First, an evacuation path cannot pass through the vertex on fire. Second, the fact that someone close to the fire may not take rational decisions when selecting a direction to escape is modeled using new kinds of evacuation paths. In this paper, we characterize the set of feasible solutions of Min P p CP-instance. Then, we propose some approximation results for Min P p CP. These results require approximation results for two variants of the (deterministic) Min p-Center problem called Min MAC p-Center and Min Partial p-Center.

压力下的概率 p 中心问题(Min P p CP)是我们最近在野火管理中引入的普通 Min p 中心问题的一个变体。问题是如何确定 p 个避难所的位置,使人们在发生火灾时到达最近的避难所所需的最大距离最小化。地形被划分为多个区域,并被建模为一个边加权图,图中顶点与区域相对应,边与相邻两个区域之间的直接连接相对应。与火灾爆发相关的风险是通过一组有限的火灾场景来模拟的。每种情况都对应一个区域(即一个顶点)爆发火灾,其主要后果是以两种方式改变疏散路径。首先,疏散路径不能经过着火顶点。其次,在选择逃生方向时,靠近火场的人可能不会做出理性的决定,这就需要使用新型疏散路径来模拟这一情况。本文描述了 Min P p CP-instance 的可行解集。然后,我们提出了 Min P p CP 的一些近似结果。这些结果需要(确定性)最小 p 中心问题的两个变体的近似结果,即最小 MAC p 中心和最小部分 p 中心。
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引用次数: 0
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Journal of Combinatorial Optimization
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