Pub Date : 2024-11-13DOI: 10.1016/j.jcss.2024.103603
Zhiyi Tang
Though embedding problems have been considered for several regular graphs [1], [2], [3], it is still an open problem for hypercube into torus [4], [2]. In the paper, we prove the conjecture mathematically and obtain the minimum wirelength of embedding for hypercube into Cartesian product of paths and/or cycles. In addition, we explain that Gray code embedding is an optimal strategy in such embedding problems.
{"title":"Embedding hypercubes into torus and Cartesian product of paths and/or cycles for minimizing wirelength","authors":"Zhiyi Tang","doi":"10.1016/j.jcss.2024.103603","DOIUrl":"10.1016/j.jcss.2024.103603","url":null,"abstract":"<div><div>Though embedding problems have been considered for several regular graphs <span><span>[1]</span></span>, <span><span>[2]</span></span>, <span><span>[3]</span></span>, it is still an open problem for hypercube into torus <span><span>[4]</span></span>, <span><span>[2]</span></span>. In the paper, we prove the conjecture mathematically and obtain the minimum wirelength of embedding for hypercube into Cartesian product of paths and/or cycles. In addition, we explain that Gray code embedding is an optimal strategy in such embedding problems.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"148 ","pages":"Article 103603"},"PeriodicalIF":1.1,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142654142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-11-05DOI: 10.1016/j.jcss.2024.103600
Jesper Nederlof, Krisztina Szilágyi
In this paper we investigate the parameterized complexity of counting and detecting small patterns in unit disk graphs: Given an n-vertex unit disk graph G with an embedding of ply p (i.e. G is an intersection graph of closed unit disks, and each point is contained in at most p disks) and a k-vertex unit disk graph P, count the number of (induced) copies of P in G. For general patterns P, we give an time algorithm for counting pattern occurrences. We show this is tight, even for ply : any time algorithm violates the Exponential Time Hypothesis (ETH). Our approach combines tools developed for planar subgraph isomorphism such as ‘efficient inclusion-exclusion’ from Nederlof (2020) [15], and ‘isomorphisms checks’ from Bodlaender et al. (2016) [5] with a different separator hierarchy and a new bound on the number of non-isomorphic separations tailored for unit disk graphs.
在本文中，我们研究了计算和检测单位盘图中小图案的参数化复杂性：给定一个具有 ply p 嵌入的 n 个顶点单位盘图 G（即 G 是封闭单位盘的交集图，且每个点最多包含在 p 个盘中）和一个 k 个顶点单位盘图 P，计算 P 在 G 中的（诱导）副本数。对于一般图案 P，我们给出了一个 2O(pk/logk)nO(1)时间的算法来计算图案出现次数。我们证明了这一算法的严密性，即使对于 ply p=2 也是如此：任何 2o(n/logn)nO(1)时间算法都违反了指数时间假说 (ETH)。我们的方法结合了为平面子图同构开发的工具，如 Nederlof (2020) [15] 的 "高效包容-排除 "和 Bodlaender 等人 (2016) [5] 的 "同构检查"，以及不同的分离器层次结构和为单位盘图量身定制的非同构分离数量新约束。
{"title":"Algorithms and Turing kernels for detecting and counting small patterns in unit disk graphs","authors":"Jesper Nederlof, Krisztina Szilágyi","doi":"10.1016/j.jcss.2024.103600","DOIUrl":"10.1016/j.jcss.2024.103600","url":null,"abstract":"<div><div>In this paper we investigate the parameterized complexity of counting and detecting small patterns in unit disk graphs: Given an <em>n</em>-vertex unit disk graph <em>G</em> with an embedding of ply <em>p</em> (i.e. <em>G</em> is an intersection graph of closed unit disks, and each point is contained in at most <em>p</em> disks) and a <em>k</em>-vertex unit disk graph <em>P</em>, count the number of (induced) copies of <em>P</em> in <em>G</em>. For general patterns <em>P</em>, we give an <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>O</mi><mo>(</mo><mi>p</mi><mi>k</mi><mo>/</mo><mi>log</mi><mo></mo><mi>k</mi><mo>)</mo></mrow></msup><msup><mrow><mi>n</mi></mrow><mrow><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msup></math></span> time algorithm for counting pattern occurrences. We show this is tight, even for ply <span><math><mi>p</mi><mo>=</mo><mn>2</mn></math></span>: any <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>o</mi><mo>(</mo><mi>n</mi><mo>/</mo><mi>log</mi><mo></mo><mi>n</mi><mo>)</mo></mrow></msup><msup><mrow><mi>n</mi></mrow><mrow><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msup></math></span> time algorithm violates the Exponential Time Hypothesis (ETH). Our approach combines tools developed for planar subgraph isomorphism such as ‘efficient inclusion-exclusion’ from Nederlof (2020) <span><span>[15]</span></span>, and ‘isomorphisms checks’ from Bodlaender et al. (2016) <span><span>[5]</span></span> with a different separator hierarchy and a new bound on the number of non-isomorphic separations tailored for unit disk graphs.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"148 ","pages":"Article 103600"},"PeriodicalIF":1.1,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142654144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-10-31DOI: 10.1016/j.jcss.2024.103601
Chris Köcher , Dietrich Kuske
A cooperating multi-pushdown system consists of a tuple of pushdown systems that can delegate the execution of recursive procedures to sub-tuples; control returns to the calling tuple once all sub-tuples finished their task. This allows the concurrent execution since disjoint sub-tuples can perform their task independently. Because of the concrete form of recursive descent into sub-tuples, the content of the multi-pushdown does not form an arbitrary tuple of words, but can be understood as a Mazurkiewicz trace. For such systems, we prove that the backwards reachability relation efficiently preserves recognizability, generalizing a result and proof technique by Bouajjani et al. for single-pushdown systems. It follows that the reachability relation is decidable for cooperating multi-pushdown systems in polynomial time and the same holds, e.g., for safety and liveness properties given by recognizable sets of configurations.
{"title":"Backwards-reachability for cooperating multi-pushdown systems","authors":"Chris Köcher , Dietrich Kuske","doi":"10.1016/j.jcss.2024.103601","DOIUrl":"10.1016/j.jcss.2024.103601","url":null,"abstract":"<div><div>A cooperating multi-pushdown system consists of a tuple of pushdown systems that can delegate the execution of recursive procedures to sub-tuples; control returns to the calling tuple once all sub-tuples finished their task. This allows the concurrent execution since disjoint sub-tuples can perform their task independently. Because of the concrete form of recursive descent into sub-tuples, the content of the multi-pushdown does not form an arbitrary tuple of words, but can be understood as a Mazurkiewicz trace. For such systems, we prove that the backwards reachability relation efficiently preserves recognizability, generalizing a result and proof technique by Bouajjani et al. for single-pushdown systems. It follows that the reachability relation is decidable for cooperating multi-pushdown systems in polynomial time and the same holds, e.g., for safety and liveness properties given by recognizable sets of configurations.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"148 ","pages":"Article 103601"},"PeriodicalIF":1.1,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142654143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-10-22DOI: 10.1016/j.jcss.2024.103596
Daniela Bubboloni , Costanza Catalano , Andrea Marino , Ana Silva
We extend the concept of out/in-branchings spanning the vertices of a digraph to temporal graphs, which are digraphs where arcs are available only at prescribed times. While the literature has focused on minimum weight/earliest arrival time Temporal Out-Branchings (tob), we solve the problem for other optimization criteria (travel duration, departure time, number of transfers, total waiting time, traveling time). For some criteria we provide a log linear algorithm for computing such branchings, while for others we prove that deciding the existence of a spanning tob is NP-complete. The same results hold for optimal temporal in-branchings. We also investigate the related problem of computing a spanning temporal subgraph with the minimum number of arcs and optimizing a chosen criterion; this problem turns out to be always NP-hard. The hardness results are quite surprising, as computing optimal paths between nodes is always polynomial-time.
{"title":"On computing optimal temporal branchings and spanning subgraphs","authors":"Daniela Bubboloni , Costanza Catalano , Andrea Marino , Ana Silva","doi":"10.1016/j.jcss.2024.103596","DOIUrl":"10.1016/j.jcss.2024.103596","url":null,"abstract":"<div><div>We extend the concept of out/in-branchings spanning the vertices of a digraph to temporal graphs, which are digraphs where arcs are available only at prescribed times. While the literature has focused on minimum weight/earliest arrival time Temporal Out-Branchings (<span>tob</span>), we solve the problem for other optimization criteria (travel duration, departure time, number of transfers, total waiting time, traveling time). For some criteria we provide a log linear algorithm for computing such branchings, while for others we prove that deciding the existence of a spanning <span>tob</span> is <span>NP</span>-complete. The same results hold for optimal temporal in-branchings. We also investigate the related problem of computing a spanning temporal subgraph with the minimum number of arcs and optimizing a chosen criterion; this problem turns out to be always <span>NP</span>-hard. The hardness results are quite surprising, as computing optimal paths between nodes is always polynomial-time.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"148 ","pages":"Article 103596"},"PeriodicalIF":1.1,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-10-21DOI: 10.1016/j.jcss.2024.103597
Bart M.P. Jansen , Jari J.H. de Kroon , Michał Włodarczyk
The celebrated notion of important separators bounds the number of small -separators in a graph which are ‘farthest from S’ in a technical sense. In this paper, we introduce a generalization of this powerful algorithmic primitive, tailored to undirected graphs, that is phrased in terms of k-secluded vertex sets: sets with an open neighborhood of size at most k. In this terminology, the bound on important separators says that there are at most maximal k-secluded connected vertex sets C containing S but disjoint from T. We generalize this statement significantly: even when we demand that avoids a finite set of forbidden induced subgraphs, the number of such maximal subgraphs is and they can be enumerated efficiently. This enumeration algorithm allows us to give improved parameterized algorithms for Connectedk-Secluded-Free Subgraph and for deleting into scattered graph classes.
著名的重要分隔符概念限定了图中在技术意义上 "离 S 最远 "的小 (S,T) 分隔符的数量。在本文中，我们针对无向图引入了这一强大算法基本原理的广义化，用 k 个排除顶点集来表述：具有大小至多为 k 的开放邻域的集合。在这个术语中，重要分隔符的约束是指最多有 4k 个最大的 k-secluded连通顶点集 C，其中包含 S 但与 T 不相交。我们对这一声明进行了显著的概括：即使我们要求 G[C] 避免有限的禁止诱导子图集 F，这种最大子图的数量也是 2O(k)，而且可以高效地枚举出来。有了这种枚举算法，我们就能给出改进的参数化算法，用于连接 k-Secluded F-Free Subgraph 和删除成分散图类。
{"title":"Single-exponential FPT algorithms for enumerating secluded F-free subgraphs and deleting to scattered graph classes","authors":"Bart M.P. Jansen , Jari J.H. de Kroon , Michał Włodarczyk","doi":"10.1016/j.jcss.2024.103597","DOIUrl":"10.1016/j.jcss.2024.103597","url":null,"abstract":"<div><div>The celebrated notion of important separators bounds the number of small <span><math><mo>(</mo><mi>S</mi><mo>,</mo><mi>T</mi><mo>)</mo></math></span>-separators in a graph which are ‘farthest from <em>S</em>’ in a technical sense. In this paper, we introduce a generalization of this powerful algorithmic primitive, tailored to undirected graphs, that is phrased in terms of <em>k-secluded</em> vertex sets: sets with an open neighborhood of size at most <em>k</em>. In this terminology, the bound on important separators says that there are at most <span><math><msup><mrow><mn>4</mn></mrow><mrow><mi>k</mi></mrow></msup></math></span> maximal <em>k</em>-secluded connected vertex sets <em>C</em> containing <em>S</em> but disjoint from <em>T</em>. We generalize this statement significantly: even when we demand that <span><math><mi>G</mi><mo>[</mo><mi>C</mi><mo>]</mo></math></span> avoids a finite set <span><math><mi>F</mi></math></span> of forbidden induced subgraphs, the number of such maximal subgraphs is <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>O</mi><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup></math></span> and they can be enumerated efficiently. This enumeration algorithm allows us to give improved parameterized algorithms for <span>Connected</span> <em>k</em><span>-Secluded</span> <span><math><mi>F</mi></math></span><span>-Free Subgraph</span> and for deleting into scattered graph classes.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"148 ","pages":"Article 103597"},"PeriodicalIF":1.1,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-10-21DOI: 10.1016/j.jcss.2024.103599
Juhi Chaudhary , Meirav Zehavi
A matching M in a graph G is an acyclic matching if the subgraph of G induced by the endpoints of the edges of M is a forest. Given a graph G and , Acyclic Matching asks whether G has an acyclic matching of size at least ℓ. In this paper, we prove that assuming , there does not exist any -approximation algorithm for Acyclic Matching that approximates it within a constant factor when parameterized by ℓ. Our reduction also asserts -inapproximability for Induced Matching and Uniquely Restricted Matching. We also consider three below-guarantee parameters for Acyclic Matching, viz. , , and , where , is the matching number, and is the independence number of G. Also, we show that Acyclic Matching does not exhibit a polynomial kernel with respect to vertex cover number (or vertex deletion distance to clique) plus the size of the matching unless .
如果 M 的边的端点所诱导的 G 子图是一个森林，那么图 G 中的匹配 M 就是非循环匹配。给定一个图 G 和 ℓ∈N，非循环匹配问 G 是否有大小至少为 ℓ 的非循环匹配。在本文中，我们证明了假设 W[1]⊈FPT 时，不存在任何 FPT 近似算法，可以在以ℓ 为参数时，以常数因子内逼近 Acyclic Matching。我们的还原也证明了诱导匹配和唯一限制匹配的 FPT 近似性。我们还考虑了 Acyclic Matching 的三个低于保证的参数，即 n2-ℓ、MM(G)-ℓ 和 IS(G)-ℓ，其中 n=V(G), MM(G) 是匹配数，IS(G) 是 G 的独立数。此外，我们还证明，除非 NP⊆coNP/poly，否则无循环匹配并不表现出关于顶点覆盖数（或顶点到小块的删除距离）加上匹配大小的多项式内核。
{"title":"Parameterized results on acyclic matchings with implications for related problems","authors":"Juhi Chaudhary , Meirav Zehavi","doi":"10.1016/j.jcss.2024.103599","DOIUrl":"10.1016/j.jcss.2024.103599","url":null,"abstract":"<div><div>A matching <em>M</em> in a graph <em>G</em> is an <em>acyclic matching</em> if the subgraph of <em>G</em> induced by the endpoints of the edges of <em>M</em> is a forest. Given a graph <em>G</em> and <span><math><mi>ℓ</mi><mo>∈</mo><mi>N</mi></math></span>, <span>Acyclic Matching</span> asks whether <em>G</em> has an acyclic matching of <em>size</em> at least <em>ℓ</em>. In this paper, we prove that assuming <span><math><mi>W</mi><mo>[</mo><mn>1</mn><mo>]</mo><mo>⊈</mo><mi>FPT</mi></math></span>, there does not exist any <span><math><mi>FPT</mi></math></span>-approximation algorithm for <span>Acyclic Matching</span> that approximates it within a constant factor when parameterized by <em>ℓ</em>. Our reduction also asserts <span><math><mi>FPT</mi></math></span>-inapproximability for <span>Induced Matching</span> and <span>Uniquely Restricted Matching</span>. We also consider three below-guarantee parameters for <span>Acyclic Matching</span>, viz. <span><math><mfrac><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>−</mo><mi>ℓ</mi></math></span>, <span><math><mrow><mi>MM</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>−</mo><mi>ℓ</mi></math></span>, and <span><math><mrow><mi>IS</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>−</mo><mi>ℓ</mi></math></span>, where <span><math><mi>n</mi><mo>=</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>, <span><math><mi>MM</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> is the <em>matching number</em>, and <span><math><mi>IS</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> is the <em>independence number</em> of <em>G</em>. Also, we show that <span>Acyclic Matching</span> does not exhibit a polynomial kernel with respect to vertex cover number (or vertex deletion distance to clique) plus the size of the matching unless <span><math><mrow><mi>NP</mi></mrow><mo>⊆</mo><mrow><mi>coNP</mi></mrow><mo>/</mo><mrow><mi>poly</mi></mrow></math></span>.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"148 ","pages":"Article 103599"},"PeriodicalIF":1.1,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-10-18DOI: 10.1016/j.jcss.2024.103598
Johannes Rauch , Dieter Rautenbach , Uéverton S. Souza
The Independent Cutset problem asks whether there is a set of vertices in a given graph that is both independent and a cutset. This problem is -complete even when the input graph is planar and has maximum degree five. We first present a -time algorithm to compute a minimum independent cutset (if any). Since the property of having an independent cutset is MSO1-expressible, our main results are concerned with structural parameterizations for the problem considering parameters incomparable with clique-width. We present -time algorithms under the following parameters: the dual of the maximum degree, the dual of the solution size, the size of a dominating set (where a dominating set is given as an additional input), the size of an odd cycle transversal, the distance to chordal graphs, and the distance to -free graphs. We close by introducing the notion of α-domination, which generalizes key ideas of this article.
{"title":"Exact and parameterized algorithms for the independent cutset problem","authors":"Johannes Rauch , Dieter Rautenbach , Uéverton S. Souza","doi":"10.1016/j.jcss.2024.103598","DOIUrl":"10.1016/j.jcss.2024.103598","url":null,"abstract":"<div><div>The <span>Independent Cutset</span> problem asks whether there is a set of vertices in a given graph that is both independent and a cutset. This problem is <figure><img></figure>-complete even when the input graph is planar and has maximum degree five. We first present a <span><math><msup><mrow><mi>O</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><msup><mrow><mn>1.4423</mn></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span>-time algorithm to compute a minimum independent cutset (if any). Since the property of having an independent cutset is MSO<sub>1</sub>-expressible, our main results are concerned with structural parameterizations for the problem considering parameters incomparable with clique-width. We present <figure><img></figure>-time algorithms under the following parameters: the dual of the maximum degree, the dual of the solution size, the size of a dominating set (where a dominating set is given as an additional input), the size of an odd cycle transversal, the distance to chordal graphs, and the distance to <span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>5</mn></mrow></msub></math></span>-free graphs. We close by introducing the notion of <em>α</em>-domination, which generalizes key ideas of this article.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"148 ","pages":"Article 103598"},"PeriodicalIF":1.1,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-10-10DOI: 10.1016/j.jcss.2024.103588
Amotz Bar-Noy , Toni Böhnlein , David Peleg , Yingli Ran , Dror Rawitz
We study the question of whether a sequence of positive integers is the degree sequence of some outerplanar graph G. If so, G is an outerplanar realization of d and d is an outerplanaric sequence. The case where is easy, as d has a realization by a forest. In this paper, we consider the family of all sequences d of even sum , where is the number of x's in d. We partition into two disjoint subfamilies, , such that every sequence in is provably non-outerplanaric, and every sequence in is given a realizing graph G enjoying a 2-page book embedding (and moreover, one of the pages is also bipartite).
我们研究的问题是：正整数序列 d=(d1,...,dn) 是否是某个外平面图 G 的度数序列？如果是，则 G 是 d 的外平面实现，d 是外平面序列。∑d≤2n-2的情况很容易，因为d有一个森林的实现。在本文中，我们考虑所有偶数和为 2n≤∑d≤4n-6-2ω1 的序列 d 的族 D，其中 ωx 是 d 中 x 的个数。我们将 D 分成两个互不相交的子系列，D=DNOP∪D2PBE，这样 DNOP 中的每个序列都是可证明的非平面外序列，而 D2PBE 中的每个序列都有一个实现图 G，享有两页书的嵌入（此外，其中一页也是双向的）。
{"title":"Approximate realizations for outerplanaric degree sequences","authors":"Amotz Bar-Noy , Toni Böhnlein , David Peleg , Yingli Ran , Dror Rawitz","doi":"10.1016/j.jcss.2024.103588","DOIUrl":"10.1016/j.jcss.2024.103588","url":null,"abstract":"<div><div>We study the question of whether a sequence <span><math><mi>d</mi><mo>=</mo><mo>(</mo><msub><mrow><mi>d</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math></span> of positive integers is the degree sequence of some outerplanar graph <em>G</em>. If so, <em>G</em> is an outerplanar realization of <em>d</em> and <em>d</em> is an outerplanaric sequence. The case where <span><math><mo>∑</mo><mi>d</mi><mo>≤</mo><mn>2</mn><mi>n</mi><mo>−</mo><mn>2</mn></math></span> is easy, as <em>d</em> has a realization by a forest. In this paper, we consider the family <span><math><mi>D</mi></math></span> of all sequences <em>d</em> of even sum <span><math><mn>2</mn><mi>n</mi><mo>≤</mo><mo>∑</mo><mi>d</mi><mo>≤</mo><mn>4</mn><mi>n</mi><mo>−</mo><mn>6</mn><mo>−</mo><mn>2</mn><msub><mrow><mi>ω</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, where <span><math><msub><mrow><mi>ω</mi></mrow><mrow><mi>x</mi></mrow></msub></math></span> is the number of <em>x</em>'s in <em>d</em>. We partition <span><math><mi>D</mi></math></span> into two disjoint subfamilies, <span><math><mi>D</mi><mo>=</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>N</mi><mi>O</mi><mi>P</mi></mrow></msub><mo>∪</mo><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn><mi>P</mi><mi>B</mi><mi>E</mi></mrow></msub></math></span>, such that every sequence in <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>N</mi><mi>O</mi><mi>P</mi></mrow></msub></math></span> is provably non-outerplanaric, and every sequence in <span><math><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn><mi>P</mi><mi>B</mi><mi>E</mi></mrow></msub></math></span> is given a realizing graph <em>G</em> enjoying a 2-page book embedding (and moreover, one of the pages is also bipartite).</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"148 ","pages":"Article 103588"},"PeriodicalIF":1.1,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-09-27DOI: 10.1016/j.jcss.2024.103587
George Mertzios , Othon Michail , George Skretas , Paul G. Spirakis , Michail Theofilatos
We study a new algorithmic process of graph growth which starts from a single initial vertex and operates in discrete time-steps, called slots. In every slot, the graph grows via two operations (i) vertex generation and (ii) edge activation. The process completes at the last slot where a (possibly empty) subset of the edges of the graph are removed. Removed edges are called excess edges. The main problem investigated in this paper is: Given a target graph G, design an algorithm that outputs a process that grows G, called a growth schedule. Additionally, we aim to minimize the total number of slots k and of excess edges ℓ used by the process. We provide both positive and negative results, with our main focus being either schedules with sub-linear number of slots or with no excess edges.
我们研究了一种新的图形增长算法过程，它从单个初始顶点开始，以离散的时间步长（称为时隙）运行。在每个时段内，图形通过两个操作（i）顶点生成和（ii）边激活进行增长。该过程在最后一个时隙完成，在该时隙中，图形的一个（可能为空）边子集被移除。被移除的边称为多余边。本文研究的主要问题是给定目标图 G，设计一种算法，输出一个使 G 增长的过程，称为增长计划。此外，我们的目标是最小化进程使用的插槽 k 和多余边 ℓ 的总数。我们提供了正反两方面的结果，重点是具有亚线性槽数或无多余边的时间表。
{"title":"The complexity of growing a graph","authors":"George Mertzios , Othon Michail , George Skretas , Paul G. Spirakis , Michail Theofilatos","doi":"10.1016/j.jcss.2024.103587","DOIUrl":"10.1016/j.jcss.2024.103587","url":null,"abstract":"<div><div>We study a new algorithmic process of graph growth which starts from a single initial vertex and operates in discrete time-steps, called <em>slots</em>. In every slot, the graph grows via two operations (i) vertex generation and (ii) edge activation. The process completes at the last slot where a (possibly empty) subset of the edges of the graph are removed. Removed edges are called <em>excess edges</em>. The main problem investigated in this paper is: Given a target graph <em>G</em>, design an algorithm that outputs a process that grows <em>G</em>, called a <em>growth schedule</em>. Additionally, we aim to minimize the total number of slots <em>k</em> and of excess edges <em>ℓ</em> used by the process. We provide both positive and negative results, with our main focus being either schedules with sub-linear number of slots or with no excess edges.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"147 ","pages":"Article 103587"},"PeriodicalIF":1.1,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142417216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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}
We develop an algorithm that combines the advantages of Priority Promotion, that is one of the leading approaches to solving large parity games in practice, with the quasi-polynomial time guarantees offered by Parys' algorithm. Hybridising these algorithms sounds both natural and difficult, as they both generalise the classic recursive algorithm in different ways that appear to be irreconcilable: while the promotion transcends the call structure, the guarantees change on each level. We show that an interface that respects both is not only effective, but also efficient.
{"title":"Priority Promotion with Parysian flair","authors":"Massimo Benerecetti , Daniele Dell'Erba , Fabio Mogavero , Sven Schewe , Dominik Wojtczak","doi":"10.1016/j.jcss.2024.103580","DOIUrl":"10.1016/j.jcss.2024.103580","url":null,"abstract":"<div><p>We develop an algorithm that combines the advantages of Priority Promotion, that is one of the leading approaches to solving large parity games in practice, with the quasi-polynomial time guarantees offered by Parys' algorithm. Hybridising these algorithms sounds both natural and difficult, as they both generalise the classic recursive algorithm in different ways that appear to be irreconcilable: while the promotion transcends the call structure, the guarantees change on each level. We show that an interface that respects both is not only effective, but also efficient.</p></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"147 ","pages":"Article 103580"},"PeriodicalIF":1.1,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022000024000758/pdfft?md5=3e785823aeb6c21ee0b0856d965cf339&pid=1-s2.0-S0022000024000758-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142150192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号