Pub Date : 2022-10-14DOI: 10.48550/arXiv.2210.07979
Yuuki Yonemoto, Yuto Nakashima, Shunsuke Inenaga, H. Bannai
One of the most fundamental method for comparing two given strings A and B is the longest common subsequence (LCS), where the task is to find (the length) of the longest common subsequence. In this paper, we address the STR-IC-LCS problem which is one of the constrained LCS problems proposed by Chen and Chao [J. Comb. Optim, 2011]. A string Z is said to be an STR-IC-LCS of three given strings A , B , and P , if Z is one of the longest common subsequences of A and B that contains P as a substring. We present a space efficient solution for the STR-IC-LCS problem. Our algorithm computes the length of an STR-IC-LCS in O ( n 2 ) time and O (( (cid:96) + 1)( n − (cid:96) + 1)) space where (cid:96) is the length of a longest common subsequence of A and B of length n . When (cid:96) = O (1) or n − (cid:96) = O (1), then our algorithm uses only linear O ( n ) space.
{"title":"Space-Efficient STR-IC-LCS Computation","authors":"Yuuki Yonemoto, Yuto Nakashima, Shunsuke Inenaga, H. Bannai","doi":"10.48550/arXiv.2210.07979","DOIUrl":"https://doi.org/10.48550/arXiv.2210.07979","url":null,"abstract":"One of the most fundamental method for comparing two given strings A and B is the longest common subsequence (LCS), where the task is to find (the length) of the longest common subsequence. In this paper, we address the STR-IC-LCS problem which is one of the constrained LCS problems proposed by Chen and Chao [J. Comb. Optim, 2011]. A string Z is said to be an STR-IC-LCS of three given strings A , B , and P , if Z is one of the longest common subsequences of A and B that contains P as a substring. We present a space efficient solution for the STR-IC-LCS problem. Our algorithm computes the length of an STR-IC-LCS in O ( n 2 ) time and O (( (cid:96) + 1)( n − (cid:96) + 1)) space where (cid:96) is the length of a longest common subsequence of A and B of length n . When (cid:96) = O (1) or n − (cid:96) = O (1), then our algorithm uses only linear O ( n ) space.","PeriodicalId":266155,"journal":{"name":"Conference on Current Trends in Theory and Practice of Informatics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129821901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-13DOI: 10.48550/arXiv.2210.06744
J. Klawitter, Felix Klesen, Moritz Niederer, A. Wolff
. We consider the problem of drawing multiple gene trees inside a single species tree in order to visualize multispecies coalescent trees. Specifically, the drawing of the species tree fills a rectangle in which each of its edges is represented by a smaller rectangle, and the gene trees are drawn as rectangular cladograms (that is, orthogonally and down-ward, with one bend per edge) inside the drawing of the species tree. As an alternative, we also consider a style where the widths of the edges of the species tree are proportional to given effective population sizes. In order to obtain readable visualizations, our aim is to minimize the number of crossings between edges of the gene trees in such drawings. We show that planar instances can be recognized in linear time and that the general problem is NP-hard. Therefore, we introduce two heuristics and give an integer linear programming (ILP) formulation that provides us with exact solutions in exponential time. We use the ILP to measure the quality of the heuristics on real-world instances. The heuristics yield surprisingly good solutions, and the ILP runs surprisingly fast.
{"title":"Visualizing Multispecies Coalescent Trees: Drawing Gene Trees Inside Species Trees","authors":"J. Klawitter, Felix Klesen, Moritz Niederer, A. Wolff","doi":"10.48550/arXiv.2210.06744","DOIUrl":"https://doi.org/10.48550/arXiv.2210.06744","url":null,"abstract":". We consider the problem of drawing multiple gene trees inside a single species tree in order to visualize multispecies coalescent trees. Specifically, the drawing of the species tree fills a rectangle in which each of its edges is represented by a smaller rectangle, and the gene trees are drawn as rectangular cladograms (that is, orthogonally and down-ward, with one bend per edge) inside the drawing of the species tree. As an alternative, we also consider a style where the widths of the edges of the species tree are proportional to given effective population sizes. In order to obtain readable visualizations, our aim is to minimize the number of crossings between edges of the gene trees in such drawings. We show that planar instances can be recognized in linear time and that the general problem is NP-hard. Therefore, we introduce two heuristics and give an integer linear programming (ILP) formulation that provides us with exact solutions in exponential time. We use the ILP to measure the quality of the heuristics on real-world instances. The heuristics yield surprisingly good solutions, and the ILP runs surprisingly fast.","PeriodicalId":266155,"journal":{"name":"Conference on Current Trends in Theory and Practice of Informatics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129529535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-11DOI: 10.48550/arXiv.2210.05384
K. Buchin, W. Evans, Fabrizio Frati, I. Kostitsyna, M. Löffler, Tim Ophelders, A. Wolff
. In this paper, we investigate crossing-free 3D morphs between planar straight-line drawings. We show that, for any two (not necessarily topologically equivalent) planar straight-line drawings of an n -vertex planar graph, there exists a piecewise-linear crossing-free 3D morph with O ( n 2 ) steps that transforms one drawing into the other. We also give some evidence why it is difficult to obtain a linear lower bound (which exists in 2D) for the number of steps of a crossing-free 3D morph.
{"title":"Morphing Planar Graph Drawings Through 3D","authors":"K. Buchin, W. Evans, Fabrizio Frati, I. Kostitsyna, M. Löffler, Tim Ophelders, A. Wolff","doi":"10.48550/arXiv.2210.05384","DOIUrl":"https://doi.org/10.48550/arXiv.2210.05384","url":null,"abstract":". In this paper, we investigate crossing-free 3D morphs between planar straight-line drawings. We show that, for any two (not necessarily topologically equivalent) planar straight-line drawings of an n -vertex planar graph, there exists a piecewise-linear crossing-free 3D morph with O ( n 2 ) steps that transforms one drawing into the other. We also give some evidence why it is difficult to obtain a linear lower bound (which exists in 2D) for the number of steps of a crossing-free 3D morph.","PeriodicalId":266155,"journal":{"name":"Conference on Current Trends in Theory and Practice of Informatics","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127478780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-10DOI: 10.48550/arXiv.2210.05019
W. Didimo, Siddharth Gupta, P. Kindermann, G. Liotta, A. Wolff, M. Zehavi
Orthogonal graph drawings are used in applications such as UML diagrams, VLSI layout, cable plans, and metro maps. We focus on drawing planar graphs and assume that we are given an emph{orthogonal representation} that describes the desired shape, but not the exact coordinates of a drawing. Our aim is to compute an orthogonal drawing on the grid that has minimum area among all grid drawings that adhere to the given orthogonal representation. This problem is called orthogonal compaction (OC) and is known to be NP-hard, even for orthogonal representations of cycles [Evans et al., 2022]. We investigate the complexity of OC with respect to several parameters. Among others, we show that OC is fixed-parameter tractable with respect to the most natural of these parameters, namely, the number of emph{kitty corners} of the orthogonal representation: the presence of pairs of kitty corners in an orthogonal representation makes the OC problem hard. Informally speaking, a pair of kitty corners is a pair of reflex corners of a face that point at each other. Accordingly, the number of kitty corners is the number of corners that are involved in some pair of kitty corners.
{"title":"Parameterized Approaches to Orthogonal Compaction","authors":"W. Didimo, Siddharth Gupta, P. Kindermann, G. Liotta, A. Wolff, M. Zehavi","doi":"10.48550/arXiv.2210.05019","DOIUrl":"https://doi.org/10.48550/arXiv.2210.05019","url":null,"abstract":"Orthogonal graph drawings are used in applications such as UML diagrams, VLSI layout, cable plans, and metro maps. We focus on drawing planar graphs and assume that we are given an emph{orthogonal representation} that describes the desired shape, but not the exact coordinates of a drawing. Our aim is to compute an orthogonal drawing on the grid that has minimum area among all grid drawings that adhere to the given orthogonal representation. This problem is called orthogonal compaction (OC) and is known to be NP-hard, even for orthogonal representations of cycles [Evans et al., 2022]. We investigate the complexity of OC with respect to several parameters. Among others, we show that OC is fixed-parameter tractable with respect to the most natural of these parameters, namely, the number of emph{kitty corners} of the orthogonal representation: the presence of pairs of kitty corners in an orthogonal representation makes the OC problem hard. Informally speaking, a pair of kitty corners is a pair of reflex corners of a face that point at each other. Accordingly, the number of kitty corners is the number of corners that are involved in some pair of kitty corners.","PeriodicalId":266155,"journal":{"name":"Conference on Current Trends in Theory and Practice of Informatics","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124067056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-08DOI: 10.48550/arXiv.2210.04080
Jared R Coleman, E. Kranakis, D. Krizanc, Oscar Morales Ponce
Two cooperating, autonomous mobile robots with arbitrary nonzero max speeds are placed at arbitrary initial positions in the plane. A remotely detonated bomb is discovered at some source location and must be moved to a safe distance away from its initial location as quickly as possible. In the Bomb Squad problem, the robots cooperate by communicating face-to-face in order to pick up the bomb from the source and carry it away to the boundary of a disk centered at the source in the shortest possible time. The goal is to specify trajectories which define the robots' paths from start to finish and their meeting points which enable face-to-face collaboration by exchanging information and passing the bomb from robot to robot. We design algorithms reflecting the robots' knowledge about orientation and each other's speed and location. In the offline case, we design an optimal algorithm. For the limited knowledge cases, we provide online algorithms which consider robots' level of agreement on orientation as per OneAxis and NoAxis models, and knowledge of the boundary as per Visible, Discoverable, and Invisible. In all cases, we provide upper and lower bounds for the competitive ratios of the online problems.
{"title":"Delivery to Safety with Two Cooperating Robots","authors":"Jared R Coleman, E. Kranakis, D. Krizanc, Oscar Morales Ponce","doi":"10.48550/arXiv.2210.04080","DOIUrl":"https://doi.org/10.48550/arXiv.2210.04080","url":null,"abstract":"Two cooperating, autonomous mobile robots with arbitrary nonzero max speeds are placed at arbitrary initial positions in the plane. A remotely detonated bomb is discovered at some source location and must be moved to a safe distance away from its initial location as quickly as possible. In the Bomb Squad problem, the robots cooperate by communicating face-to-face in order to pick up the bomb from the source and carry it away to the boundary of a disk centered at the source in the shortest possible time. The goal is to specify trajectories which define the robots' paths from start to finish and their meeting points which enable face-to-face collaboration by exchanging information and passing the bomb from robot to robot. We design algorithms reflecting the robots' knowledge about orientation and each other's speed and location. In the offline case, we design an optimal algorithm. For the limited knowledge cases, we provide online algorithms which consider robots' level of agreement on orientation as per OneAxis and NoAxis models, and knowledge of the boundary as per Visible, Discoverable, and Invisible. In all cases, we provide upper and lower bounds for the competitive ratios of the online problems.","PeriodicalId":266155,"journal":{"name":"Conference on Current Trends in Theory and Practice of Informatics","volume":"387 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133463157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-05DOI: 10.48550/arXiv.2210.02121
Filippos Christodoulou, S. Nikoletseas, C. Raptopoulos, P. Spirakis
In a random intersection graph $G_{n,m,p}$, each of $n$ vertices selects a random subset of a set of $m$ labels by including each label independently with probability $p$ and edges are drawn between vertices that have at least one label in common. Among other applications, such graphs have been used to model social networks, in which individuals correspond to vertices and various features (e.g. ideas, interests) correspond to labels; individuals sharing at least one common feature are connected and this is abstracted by edges in random intersection graphs. In this paper, we consider the problem of finding maximum cliques when the input graph is $G_{n,m,p}$. Current algorithms for this problem are successful with high probability only for relatively sparse instances, leaving the dense case mostly unexplored. We present a spectral algorithm for finding large cliques that processes vertices according to respective values in the second largest eigenvector of the adjacency matrix of induced subgraphs of the input graph corresponding to common neighbors of small cliques. Leveraging on the Single Label Clique Theorem from [15], we were able to construct random instances, without the need to externally plant a large clique in the input graph. In particular, we used label choices to determine the maximum clique and then concealed label information by just giving the adjacency matrix of $G_{n, m, p}$ as input to the algorithm. Our experimental evaluation showed that our spectral algorithm clearly outperforms existing polynomial time algorithms, both with respect to the failure probability and the approximation guarantee metrics, especially in the dense regime, thus suggesting that spectral properties of random intersection graphs may be also used to construct efficient algorithms for other NP-hard graph theoretical problems as well.
在一个随机相交图$G_{n,m,p}$中，$n$顶点中的每一个都以$p$的概率独立包含每个标签，从而选择$m$标签集合中的一个随机子集，并且在至少有一个共同标签的顶点之间绘制边。在其他应用中，这样的图已经被用来模拟社会网络，其中个体对应于顶点，各种特征(例如想法，兴趣)对应于标签;具有至少一个共同特征的个体是连通的，这是用随机相交图中的边抽象出来的。本文研究了当输入图为$G_{n,m,p}$时，求最大团的问题。目前这个问题的算法只有在相对稀疏的情况下才有高概率成功，而在密集的情况下大多没有被探索。我们提出了一种用于寻找大团的谱算法，该算法根据与小团的共同邻居对应的输入图的诱导子图邻接矩阵的第二大特征向量中的相应值处理顶点。利用[15]中的单标签团定理，我们能够构建随机实例，而不需要在输入图中外部植入一个大的团。特别是，我们使用标签选择来确定最大团，然后通过仅将邻接矩阵$G_{n, m, p}$作为算法的输入来隐藏标签信息。我们的实验评估表明，我们的谱算法在失效概率和近似保证度量方面明显优于现有的多项式时间算法，特别是在密集区域，这表明随机相交图的谱性质也可以用于构建其他NP-hard图理论问题的高效算法。
{"title":"A spectral algorithm for finding maximum cliques in dense random intersection graphs","authors":"Filippos Christodoulou, S. Nikoletseas, C. Raptopoulos, P. Spirakis","doi":"10.48550/arXiv.2210.02121","DOIUrl":"https://doi.org/10.48550/arXiv.2210.02121","url":null,"abstract":"In a random intersection graph $G_{n,m,p}$, each of $n$ vertices selects a random subset of a set of $m$ labels by including each label independently with probability $p$ and edges are drawn between vertices that have at least one label in common. Among other applications, such graphs have been used to model social networks, in which individuals correspond to vertices and various features (e.g. ideas, interests) correspond to labels; individuals sharing at least one common feature are connected and this is abstracted by edges in random intersection graphs. In this paper, we consider the problem of finding maximum cliques when the input graph is $G_{n,m,p}$. Current algorithms for this problem are successful with high probability only for relatively sparse instances, leaving the dense case mostly unexplored. We present a spectral algorithm for finding large cliques that processes vertices according to respective values in the second largest eigenvector of the adjacency matrix of induced subgraphs of the input graph corresponding to common neighbors of small cliques. Leveraging on the Single Label Clique Theorem from [15], we were able to construct random instances, without the need to externally plant a large clique in the input graph. In particular, we used label choices to determine the maximum clique and then concealed label information by just giving the adjacency matrix of $G_{n, m, p}$ as input to the algorithm. Our experimental evaluation showed that our spectral algorithm clearly outperforms existing polynomial time algorithms, both with respect to the failure probability and the approximation guarantee metrics, especially in the dense regime, thus suggesting that spectral properties of random intersection graphs may be also used to construct efficient algorithms for other NP-hard graph theoretical problems as well.","PeriodicalId":266155,"journal":{"name":"Conference on Current Trends in Theory and Practice of Informatics","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132898522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-04DOI: 10.48550/arXiv.2208.02766
Sushmita Gupta, P. Jain, Sanjay Seetharaman
In this paper, we study some multiagent variants of the knapsack problem. Fluschnik et al. [AAAI 2019] considered the model in which every agent assigns some utility to every item. They studied three preference aggregation rules for finding a subset (knapsack) of items: individually best, diverse, and Nash-welfare-based. Informally, diversity is achieved by satisfying as many voters as possible. Motivated by the application of aggregation operators in multiwinner elections, we extend the study from diverse aggregation rule to Median and Best scoring functions. We study the computational and parameterized complexity of the problem with respect to some natural parameters, namely, the number of voters, the number of items, and the distance from an easy instance. We also study the complexity of the problem under domain restrictions. Furthermore, we present significantly faster parameterized algorithms with respect to the number of voters for the diverse aggregation rule.
{"title":"More Effort Towards Multiagent Knapsack","authors":"Sushmita Gupta, P. Jain, Sanjay Seetharaman","doi":"10.48550/arXiv.2208.02766","DOIUrl":"https://doi.org/10.48550/arXiv.2208.02766","url":null,"abstract":"In this paper, we study some multiagent variants of the knapsack problem. Fluschnik et al. [AAAI 2019] considered the model in which every agent assigns some utility to every item. They studied three preference aggregation rules for finding a subset (knapsack) of items: individually best, diverse, and Nash-welfare-based. Informally, diversity is achieved by satisfying as many voters as possible. Motivated by the application of aggregation operators in multiwinner elections, we extend the study from diverse aggregation rule to Median and Best scoring functions. We study the computational and parameterized complexity of the problem with respect to some natural parameters, namely, the number of voters, the number of items, and the distance from an easy instance. We also study the complexity of the problem under domain restrictions. Furthermore, we present significantly faster parameterized algorithms with respect to the number of voters for the diverse aggregation rule.","PeriodicalId":266155,"journal":{"name":"Conference on Current Trends in Theory and Practice of Informatics","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115500076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-14DOI: 10.48550/arXiv.2203.07401
Emmanuel Arrighi, Niels Gruttemeier, Nils Morawietz, Frank Sommer, Petra Wolf
We study the computational complexity of determining structural properties of edge periodic temporal graphs (EPGs). EPGs are time-varying graphs that compactly represent periodic behavior of components of a dynamic network, for example, train schedules on a rail network. In EPGs, for each edge $e$ of the graph, a binary string $s_e$ determines in which time steps the edge is present, namely $e$ is present in time step $t$ if and only if $s_e$ contains a $1$ at position $t mod |s_e|$. Due to this periodicity, EPGs serve as very compact representations of complex periodic systems and can even be exponentially smaller than classic temporal graphs representing one period of the same system, as the latter contain the whole sequence of graphs explicitly. In this paper, we study the computational complexity of fundamental questions of the new concept of EPGs such as what is the shortest traversal time between two vertices; is there a time step in which the graph (1) is minor-free; (2) contains a minor; (3) is subgraph-free; (4) contains a subgraph; with respect to a given minor or subgraph. We give a detailed parameterized analysis for multiple combinations of parameters for the problems stated above including several parameterized algorithms.
研究了确定边缘周期时间图(EPGs)结构性质的计算复杂度。epg是时变图，它紧凑地表示动态网络组件的周期性行为，例如，铁路网络上的列车时刻表。在EPGs中，对于图的每条边$e$，一个二进制字符串$s_e$决定了这条边出现在哪个时间步长，即$e$出现在时间步长$t$当且仅当$s_e$在位置$t mod |s_e|$上包含$1$。由于这种周期性，epg作为复杂周期系统的非常紧凑的表示，甚至可以比表示同一系统的一个周期的经典时间图指数小，因为后者显式地包含了整个图序列。在本文中，我们研究了epg新概念的基本问题的计算复杂度，如两个顶点之间的最短穿越时间是多少;是否存在图(1)不存在次元的时间步长;(二)有未成年人的;(3)无子图;(4)包含子图;相对于一个给定的子图或子图。我们对上述问题的多个参数组合进行了详细的参数化分析，包括几种参数化算法。
{"title":"Multi-Parameter Analysis of Finding Minors and Subgraphs in Edge Periodic Temporal Graphs","authors":"Emmanuel Arrighi, Niels Gruttemeier, Nils Morawietz, Frank Sommer, Petra Wolf","doi":"10.48550/arXiv.2203.07401","DOIUrl":"https://doi.org/10.48550/arXiv.2203.07401","url":null,"abstract":"We study the computational complexity of determining structural properties of edge periodic temporal graphs (EPGs). EPGs are time-varying graphs that compactly represent periodic behavior of components of a dynamic network, for example, train schedules on a rail network. In EPGs, for each edge $e$ of the graph, a binary string $s_e$ determines in which time steps the edge is present, namely $e$ is present in time step $t$ if and only if $s_e$ contains a $1$ at position $t mod |s_e|$. Due to this periodicity, EPGs serve as very compact representations of complex periodic systems and can even be exponentially smaller than classic temporal graphs representing one period of the same system, as the latter contain the whole sequence of graphs explicitly. In this paper, we study the computational complexity of fundamental questions of the new concept of EPGs such as what is the shortest traversal time between two vertices; is there a time step in which the graph (1) is minor-free; (2) contains a minor; (3) is subgraph-free; (4) contains a subgraph; with respect to a given minor or subgraph. We give a detailed parameterized analysis for multiple combinations of parameters for the problems stated above including several parameterized algorithms.","PeriodicalId":266155,"journal":{"name":"Conference on Current Trends in Theory and Practice of Informatics","volume":"120 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131427310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-16DOI: 10.1007/978-3-031-23101-8_13
K. Jansen, K. Kahler
{"title":"On the Complexity of Scheduling Problems with a Fixed Number of Parallel Identical Machines","authors":"K. Jansen, K. Kahler","doi":"10.1007/978-3-031-23101-8_13","DOIUrl":"https://doi.org/10.1007/978-3-031-23101-8_13","url":null,"abstract":"","PeriodicalId":266155,"journal":{"name":"Conference on Current Trends in Theory and Practice of Informatics","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125828459","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-05-29DOI: 10.1007/978-3-030-67731-2_43
L. Bulteau, G. Fertin, Géraldine Jean, Christian Komusiewicz
{"title":"Sorting by Multi-cut Rearrangements","authors":"L. Bulteau, G. Fertin, Géraldine Jean, Christian Komusiewicz","doi":"10.1007/978-3-030-67731-2_43","DOIUrl":"https://doi.org/10.1007/978-3-030-67731-2_43","url":null,"abstract":"","PeriodicalId":266155,"journal":{"name":"Conference on Current Trends in Theory and Practice of Informatics","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117259652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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