Pub Date : 2023-06-09DOI: 10.1142/s0129054123500119
Hosein Salami, Mostafa Nouri-Baygi
Let [Formula: see text] be the complete Euclidean graph on a set of points embedded in the plane. Given a constant [Formula: see text], a spanning subgraph [Formula: see text] of [Formula: see text] is said to be a [Formula: see text]-spanner, or simply a spanner, if for any pair of nodes [Formula: see text], [Formula: see text] in [Formula: see text] there exists a [Formula: see text]-path in [Formula: see text], i.e., a path between [Formula: see text] and [Formula: see text] whose length is at most [Formula: see text] times their distance in [Formula: see text]. Gap-greedy spanner, proposed by Arya and Smid, is a light weight and bounded degree spanner in which a pair of points [Formula: see text] is guaranteed to have a [Formula: see text]-path, if there exists at least one edge with some special criteria in the spanner. Existing algorithms for computing the gap-greedy spanner determine the existence of such an edge for each pair of points by examining the edges of the spanner, which takes [Formula: see text] time, however in this paper, we have presented a method by which this task can be done in [Formula: see text] time. Using the proposed method and well-separated pair decomposition, we have proposed a linear-space algorithm that can compute the gap-greedy spanner in [Formula: see text] time. How to use the well-separated pair decomposition to compute this spanner was proposed by Bakhshesh and Farshi, however using an example, we have shown that one of the algorithms they have proposed for this purpose is incorrect. We have performed various experiments to measure the duration and amount of memory used by the algorithms for computing this spanner. The results of these experiments showed that the proposed method, without a significant effect on the amount of memory consumed compared to previous algorithms, leads to a significant acceleration in the construction time of this spanner.
{"title":"A Simple and Efficient Method for Accelerating Construction of the Gap-Greedy Spanner","authors":"Hosein Salami, Mostafa Nouri-Baygi","doi":"10.1142/s0129054123500119","DOIUrl":"https://doi.org/10.1142/s0129054123500119","url":null,"abstract":"Let [Formula: see text] be the complete Euclidean graph on a set of points embedded in the plane. Given a constant [Formula: see text], a spanning subgraph [Formula: see text] of [Formula: see text] is said to be a [Formula: see text]-spanner, or simply a spanner, if for any pair of nodes [Formula: see text], [Formula: see text] in [Formula: see text] there exists a [Formula: see text]-path in [Formula: see text], i.e., a path between [Formula: see text] and [Formula: see text] whose length is at most [Formula: see text] times their distance in [Formula: see text]. Gap-greedy spanner, proposed by Arya and Smid, is a light weight and bounded degree spanner in which a pair of points [Formula: see text] is guaranteed to have a [Formula: see text]-path, if there exists at least one edge with some special criteria in the spanner. Existing algorithms for computing the gap-greedy spanner determine the existence of such an edge for each pair of points by examining the edges of the spanner, which takes [Formula: see text] time, however in this paper, we have presented a method by which this task can be done in [Formula: see text] time. Using the proposed method and well-separated pair decomposition, we have proposed a linear-space algorithm that can compute the gap-greedy spanner in [Formula: see text] time. How to use the well-separated pair decomposition to compute this spanner was proposed by Bakhshesh and Farshi, however using an example, we have shown that one of the algorithms they have proposed for this purpose is incorrect. We have performed various experiments to measure the duration and amount of memory used by the algorithms for computing this spanner. The results of these experiments showed that the proposed method, without a significant effect on the amount of memory consumed compared to previous algorithms, leads to a significant acceleration in the construction time of this spanner.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45713547","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 : 2023-05-31DOI: 10.1142/s0129054123470019
R. Nishat, S. Whitesides
We study reconfiguration of simple Hamiltonian cycles in a rectangular grid graph [Formula: see text], where the Hamiltonian cycle in each step of the reconfiguration connects every internal vertex of [Formula: see text] to a boundary vertex by a single straight line segment. We introduce two operations, flip and transpose, which are local to the grid. We show that any simple cycle of [Formula: see text] can be reconfigured to any other simple cycle of [Formula: see text] using [Formula: see text] flip and transpose operations. Our result proves that the simple Hamiltonian cycle graph [Formula: see text] is connected with respect to those two operations and has diameter [Formula: see text].
{"title":"Reconfiguration of Hamiltonian Cycles in Rectangular Grid Graphs","authors":"R. Nishat, S. Whitesides","doi":"10.1142/s0129054123470019","DOIUrl":"https://doi.org/10.1142/s0129054123470019","url":null,"abstract":"We study reconfiguration of simple Hamiltonian cycles in a rectangular grid graph [Formula: see text], where the Hamiltonian cycle in each step of the reconfiguration connects every internal vertex of [Formula: see text] to a boundary vertex by a single straight line segment. We introduce two operations, flip and transpose, which are local to the grid. We show that any simple cycle of [Formula: see text] can be reconfigured to any other simple cycle of [Formula: see text] using [Formula: see text] flip and transpose operations. Our result proves that the simple Hamiltonian cycle graph [Formula: see text] is connected with respect to those two operations and has diameter [Formula: see text].","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43642684","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 : 2023-05-23DOI: 10.1142/s0129054123420030
Siu-Wing Cheng
Consider a directed temporal graph [Formula: see text] with time ranges on the edges. There can be more than one range on an edge, and each range carries a positive traversal time. Let [Formula: see text] and let [Formula: see text] be the total number of time ranges in [Formula: see text]. We assume that [Formula: see text]. We study the problem of computing shortest journeys that start from a fixed source vertex [Formula: see text] within a given time interval [Formula: see text], where the cost of a journey is equal to the sum of traversal times of the edges on it at the times of crossing those edges. We can construct in [Formula: see text] time a data structure of size [Formula: see text] such that for any vertex [Formula: see text] and any time [Formula: see text], we can report in [Formula: see text] time the cost of the shortest journey that starts from [Formula: see text] within [Formula: see text] and arrives at [Formula: see text] no later than [Formula: see text]. The journey achieving the reported cost can be produced in time linear in its complexity.
{"title":"Shortest Journeys in Directed Temporal Graphs","authors":"Siu-Wing Cheng","doi":"10.1142/s0129054123420030","DOIUrl":"https://doi.org/10.1142/s0129054123420030","url":null,"abstract":"Consider a directed temporal graph [Formula: see text] with time ranges on the edges. There can be more than one range on an edge, and each range carries a positive traversal time. Let [Formula: see text] and let [Formula: see text] be the total number of time ranges in [Formula: see text]. We assume that [Formula: see text]. We study the problem of computing shortest journeys that start from a fixed source vertex [Formula: see text] within a given time interval [Formula: see text], where the cost of a journey is equal to the sum of traversal times of the edges on it at the times of crossing those edges. We can construct in [Formula: see text] time a data structure of size [Formula: see text] such that for any vertex [Formula: see text] and any time [Formula: see text], we can report in [Formula: see text] time the cost of the shortest journey that starts from [Formula: see text] within [Formula: see text] and arrives at [Formula: see text] no later than [Formula: see text]. The journey achieving the reported cost can be produced in time linear in its complexity.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47399952","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 : 2023-05-22DOI: 10.1142/s0129054123420042
Carla Binucci, Emilio Di Giacomo, Michael Kaufmann, Giuseppe Liotta, Alessandra Tappini
This paper studies a packing problem in the so-called beyond-planar setting, that is when the host graph is “almost-planar” in some sense. Precisely, we consider the case that the host graph is [Formula: see text]-planar, i.e., it admits an embedding with at most [Formula: see text] crossings per edge, and focus on families of [Formula: see text]-regular caterpillars, that are caterpillars whose non-leaf vertices have the same degree [Formula: see text]. We study the dependency of [Formula: see text] from the number [Formula: see text] of caterpillars that are packed, both in the case that these caterpillars are all isomorphic to one another (in which case the packing is called placement) and when they are not. We give necessary and sufficient conditions for the placement of [Formula: see text] [Formula: see text]-regular caterpillars and sufficient conditions for the packing of a set of [Formula: see text]-, [Formula: see text]-, [Formula: see text], [Formula: see text]-regular caterpillars such that the degree [Formula: see text] and the degree [Formula: see text] of the non-leaf vertices can differ from one caterpillar to another, for [Formula: see text], [Formula: see text].
{"title":"k-Planar Placement and Packing of Δ-Regular Caterpillars","authors":"Carla Binucci, Emilio Di Giacomo, Michael Kaufmann, Giuseppe Liotta, Alessandra Tappini","doi":"10.1142/s0129054123420042","DOIUrl":"https://doi.org/10.1142/s0129054123420042","url":null,"abstract":"This paper studies a packing problem in the so-called beyond-planar setting, that is when the host graph is “almost-planar” in some sense. Precisely, we consider the case that the host graph is [Formula: see text]-planar, i.e., it admits an embedding with at most [Formula: see text] crossings per edge, and focus on families of [Formula: see text]-regular caterpillars, that are caterpillars whose non-leaf vertices have the same degree [Formula: see text]. We study the dependency of [Formula: see text] from the number [Formula: see text] of caterpillars that are packed, both in the case that these caterpillars are all isomorphic to one another (in which case the packing is called placement) and when they are not. We give necessary and sufficient conditions for the placement of [Formula: see text] [Formula: see text]-regular caterpillars and sufficient conditions for the packing of a set of [Formula: see text]-, [Formula: see text]-, [Formula: see text], [Formula: see text]-regular caterpillars such that the degree [Formula: see text] and the degree [Formula: see text] of the non-leaf vertices can differ from one caterpillar to another, for [Formula: see text], [Formula: see text].","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":"83 8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135381360","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 : 2023-05-22DOI: 10.1142/s0129054123450028
Maria Pittou, George Rahonis
In this paper, we propose a logic-based characterization of uncertainty in architectures of parametric component-based systems, where the parameter is the number of instances of each component type. For this, we firstly introduce an extended propositional interaction logic over De Morgan algebras and we show that its formulas can encode the uncertainty of several architectures applied in systems with a finite number of components. In turn, we introduce a first-order extended interaction logic over De Morgan algebras which is applied for modelling uncertainty in the interactions of well-known parametric architectures. Moreover, we prove that the equivalence problem for a large class of formulas of that logic is decidable in doubly exponential time by providing an effective translation to fuzzy recognizable series. For any such formula over a totally ordered De Morgan algebra, we further prove that we can compute in exponential time the set of sequences of parametric fuzzy interactions which ensure the trustworthiness of the formula according to a particular threshold.
{"title":"Modelling Uncertainty in Architectures of Parametric Component-Based Systems","authors":"Maria Pittou, George Rahonis","doi":"10.1142/s0129054123450028","DOIUrl":"https://doi.org/10.1142/s0129054123450028","url":null,"abstract":"In this paper, we propose a logic-based characterization of uncertainty in architectures of parametric component-based systems, where the parameter is the number of instances of each component type. For this, we firstly introduce an extended propositional interaction logic over De Morgan algebras and we show that its formulas can encode the uncertainty of several architectures applied in systems with a finite number of components. In turn, we introduce a first-order extended interaction logic over De Morgan algebras which is applied for modelling uncertainty in the interactions of well-known parametric architectures. Moreover, we prove that the equivalence problem for a large class of formulas of that logic is decidable in doubly exponential time by providing an effective translation to fuzzy recognizable series. For any such formula over a totally ordered De Morgan algebra, we further prove that we can compute in exponential time the set of sequences of parametric fuzzy interactions which ensure the trustworthiness of the formula according to a particular threshold.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47166004","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 : 2023-05-20DOI: 10.1142/s0129054123500090
A. Berin Greeni, R. Sundara Rajan, Paul Immanuel
The technique used in studying the computational capabilities of interconnection networks and task distribution is graph embedding. Based on the recursively constructed graphs, the hypercube network is popular for its structure. Many variants of hypercube are considered in the literature. Augmented cube is considered as one of the best variants of hypercube as it holds many desirable properties like optimal routing in linear time complexity, vertex symmetricity, wide diameter and maximum connectivity. Our work deals with the exact wirelength, when augmented cube is embedded into certain tree and windmill structures.
{"title":"Embedding Augmented Cube into Certain Trees and Windmill Graphs","authors":"A. Berin Greeni, R. Sundara Rajan, Paul Immanuel","doi":"10.1142/s0129054123500090","DOIUrl":"https://doi.org/10.1142/s0129054123500090","url":null,"abstract":"The technique used in studying the computational capabilities of interconnection networks and task distribution is graph embedding. Based on the recursively constructed graphs, the hypercube network is popular for its structure. Many variants of hypercube are considered in the literature. Augmented cube is considered as one of the best variants of hypercube as it holds many desirable properties like optimal routing in linear time complexity, vertex symmetricity, wide diameter and maximum connectivity. Our work deals with the exact wirelength, when augmented cube is embedded into certain tree and windmill structures.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48579451","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 : 2023-05-20DOI: 10.1142/s0129054123020033
M. Droste, George Rahonis, A. Salomaa
{"title":"Special Issue — International Colloquium Recent Advances of Quantitative Models in Computer Science (RAQM 2021): Preface","authors":"M. Droste, George Rahonis, A. Salomaa","doi":"10.1142/s0129054123020033","DOIUrl":"https://doi.org/10.1142/s0129054123020033","url":null,"abstract":"","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45518363","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 : 2023-05-09DOI: 10.1142/s0129054123410058
Tom Davot, R. Giroudeau, J. König
In our modern societies, a certain number of people do not own a car, by choice or by obligation. For some trips, there is no or few alternatives to the car. One way to make these trips possible for these people is to be transported by others who have already planned their trips. We propose to model this problem using as path-finding problem in a list edge-colored graph. This problem is a generalization of the [Formula: see text]-path problem, studied by Böhmová et al. We consider two optimization functions: minimizing the number of color changes and minimizing the number of colors. We study for the previous problems, the classic complexity (polynomial-case, NP-completeness, hardness of approximation) and parameter complexity (W[2]-hardness) even in restricted cases. We also propose a lower bound for exact algorithm. On the positive side we provide a polynomial-time approximation algorithm and a FPT algorithm.
{"title":"On the Shared Transportation Problem: Computational Hardness and Exact Approach","authors":"Tom Davot, R. Giroudeau, J. König","doi":"10.1142/s0129054123410058","DOIUrl":"https://doi.org/10.1142/s0129054123410058","url":null,"abstract":"In our modern societies, a certain number of people do not own a car, by choice or by obligation. For some trips, there is no or few alternatives to the car. One way to make these trips possible for these people is to be transported by others who have already planned their trips. We propose to model this problem using as path-finding problem in a list edge-colored graph. This problem is a generalization of the [Formula: see text]-path problem, studied by Böhmová et al. We consider two optimization functions: minimizing the number of color changes and minimizing the number of colors. We study for the previous problems, the classic complexity (polynomial-case, NP-completeness, hardness of approximation) and parameter complexity (W[2]-hardness) even in restricted cases. We also propose a lower bound for exact algorithm. On the positive side we provide a polynomial-time approximation algorithm and a FPT algorithm.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46776841","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 : 2023-05-09DOI: 10.1142/s0129054123410022
Yunlong Liu, Yixuan Li, Jingui Huang
The linear layout of graphs problem asks, given a graph [Formula: see text] and a positive integer [Formula: see text], whether [Formula: see text] admits a layout consisting of a linear ordering of its vertices and a partition of its edges into [Formula: see text] sets such that the edges in each set meet some special requirements. Specific linear layouts include [Formula: see text]-stack layout, [Formula: see text]-queue layout, [Formula: see text]-arch layout, mixed [Formula: see text]-stack [Formula: see text]-queue layout and others. In this paper, we present a unified approach for kernelization of these linear layout problems parameterized by the vertex cover number [Formula: see text] of the input graph. The key point underlying our approach is to partition each set of related vertices into two distinct subsets with respect to the specific layouts, which immediately leads to some efficient reduction rules. We first apply this approach to the mixed [Formula: see text]-stack [Formula: see text]-queue layout problem and show that it admits a kernel of size [Formula: see text], which results in an algorithm running in time [Formula: see text], where [Formula: see text] denotes the size of the input graph. Our work does not only confirm the existence of a fixed-parameter tractable algorithm for this problem mentioned by Bhore et al. (J. Graph Algorithms Appl. 2022), but also derives new results for the [Formula: see text]-stack layout problem and for the [Formula: see text]-queue layout problem respectively. We also employ this approach to the upward [Formula: see text]-stack layout problem and obtain a new result improving that presented by Bhore et al. (GD 2021). Last but not least, we use this approach to the [Formula: see text]-arch layout problem and obtain a similar result.
{"title":"Vertex-Bipartition: A Unified Approach for Kernelization of Graph Linear Layout Problems Parameterized by Vertex Cover","authors":"Yunlong Liu, Yixuan Li, Jingui Huang","doi":"10.1142/s0129054123410022","DOIUrl":"https://doi.org/10.1142/s0129054123410022","url":null,"abstract":"The linear layout of graphs problem asks, given a graph [Formula: see text] and a positive integer [Formula: see text], whether [Formula: see text] admits a layout consisting of a linear ordering of its vertices and a partition of its edges into [Formula: see text] sets such that the edges in each set meet some special requirements. Specific linear layouts include [Formula: see text]-stack layout, [Formula: see text]-queue layout, [Formula: see text]-arch layout, mixed [Formula: see text]-stack [Formula: see text]-queue layout and others. In this paper, we present a unified approach for kernelization of these linear layout problems parameterized by the vertex cover number [Formula: see text] of the input graph. The key point underlying our approach is to partition each set of related vertices into two distinct subsets with respect to the specific layouts, which immediately leads to some efficient reduction rules. We first apply this approach to the mixed [Formula: see text]-stack [Formula: see text]-queue layout problem and show that it admits a kernel of size [Formula: see text], which results in an algorithm running in time [Formula: see text], where [Formula: see text] denotes the size of the input graph. Our work does not only confirm the existence of a fixed-parameter tractable algorithm for this problem mentioned by Bhore et al. (J. Graph Algorithms Appl. 2022), but also derives new results for the [Formula: see text]-stack layout problem and for the [Formula: see text]-queue layout problem respectively. We also employ this approach to the upward [Formula: see text]-stack layout problem and obtain a new result improving that presented by Bhore et al. (GD 2021). Last but not least, we use this approach to the [Formula: see text]-arch layout problem and obtain a similar result.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43743124","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 : 2023-05-09DOI: 10.1142/s0129054123420017
Luca Grilli, Seok-Hee Hong, Jan Kratochvíl, Ignaz Rutter
We study the problem of drawing simultaneously embedded graphs with few bends. We show that for any simultaneous embedding with fixed edges (Sefe) of two graphs, there exists a corresponding drawing realizing this embedding such that common edges are drawn as straight-line segments and each exclusive edge has a constant number of bends. If the common graph is biconnected and induced, a straight-line drawing exists. This yields the first efficient testing algorithm for simultaneous geometric embedding (Sge) for a non-trivial class of graphs.
{"title":"Drawing Simultaneously Embedded Graphs with Few Bends","authors":"Luca Grilli, Seok-Hee Hong, Jan Kratochvíl, Ignaz Rutter","doi":"10.1142/s0129054123420017","DOIUrl":"https://doi.org/10.1142/s0129054123420017","url":null,"abstract":"We study the problem of drawing simultaneously embedded graphs with few bends. We show that for any simultaneous embedding with fixed edges (Sefe) of two graphs, there exists a corresponding drawing realizing this embedding such that common edges are drawn as straight-line segments and each exclusive edge has a constant number of bends. If the common graph is biconnected and induced, a straight-line drawing exists. This yields the first efficient testing algorithm for simultaneous geometric embedding (Sge) for a non-trivial class of graphs.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135711166","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：