Journal of Computer and System Sciences最新文献

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On the complexity of computing the co-lexicographic width of a regular language 正则语言共词典宽度计算的复杂性

IF 0.9 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences

Pub Date : 2026-01-23 DOI: 10.1016/j.jcss.2026.103759

Ruben Becker , Davide Cenzato , Sung-Hwan Kim , Tomasz Kociumaka , Bojana Kodric , Alberto Policriti , Nicola Prezza

Co-lex partial orders (Cotumaccio and Prezza (2021) [9] and Cotumaccio et al. (2023) [8]) are a powerful tool to index finite automata generalizing Wheeler orders (Gagie et al. (2017) [14]). The co-lex width p of an automaton measures how sortable its states are w.r.t. the co-lexicographic order among its accepted strings. Automata of co-lex width p can be compressed to

O (\log p)

bits per edge and admit regular expression matching in time proportional to

p^{2}

per matched character. The deterministic co-lex width of a regular language

L

is the smallest width of such a co-lex order, among all DFAs recognizing

L

. Since languages of small co-lex width admit efficient solutions to hard computational problems, computing the co-lex width is relevant in applications. Previous work showed that the deterministic co-lex width p of a language

L

can be computed in

m^{O (p)}

for a DFA

A

with m transitions accepting

L

. For constant p (in particular Wheeler languages, where

p = 1

), the constant in the exponent is large and the exact complexity remains unknown. In this work, we show that one can decide in

O (m^{p})

if the deterministic co-lex width of the language recognized by a given minimum DFA is strictly smaller than

p \geq 2

. We complement this with a matching conditional lower bound based on the Strong Exponential Time Hypothesis. Hence, our paper essentially settles the complexity of the problem.

Co-lex偏阶(Cotumaccio and Prezza（2021)[9]和Cotumaccio et al.(2023)[8]）是索引有限自动机泛化Wheeler阶（Gagie et al.(2017)[14]）的强大工具。自动机的协词法宽度p衡量其状态的可排序程度，而不是其接受的字符串之间的协词法顺序。协环宽度为p的自动机可以被压缩到每条边O（log (p)）比特，并且允许正则表达式匹配在时间上与每个匹配字符p2成正比。在所有识别L的dfa中，正则语言L的确定性协lex宽度是该协lex阶的最小宽度。由于较小协lex宽度的语言可以有效地解决难计算问题，因此计算协lex宽度在应用中是相关的。先前的工作表明，对于接受L的m个转换的DFA a，语言L的确定性协lex宽度p可以用mO(p)来计算。对于常数p（特别是惠勒语言，其中p=1），指数中的常数很大，确切的复杂性仍然未知。在这项工作中，我们证明了如果给定最小DFA识别的语言的确定性协lex宽度严格小于p≥2，则可以在O（mp）中确定。我们补充了一个基于强指数时间假设的匹配条件下界。因此，我们的论文基本上解决了这个问题的复杂性。

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引用次数: 0

Complexity of deciding the equality of matching numbers 确定匹配数相等的复杂性

IF 0.9 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences

Pub Date : 2026-01-22 DOI: 10.1016/j.jcss.2026.103760

Guilherme C.M. Gomes , Bruno P. Masquio , Paulo E.D. Pinto , Dieter Rautenbach , Vinicius F. dos Santos , Jayme L. Szwarcfiter , Florian Werner

A matching is said to be disconnected if the saturated vertices induce a disconnected subgraph and induced if the saturated vertices induce a 1-regular graph. The disconnected and induced matching numbers are defined as the maximum cardinality of such matchings, respectively, and are known to be NP-hard to compute. In this paper, we study the relationship between these two parameters and the matching number. In particular, we discuss the complexity of two decision problems; first: deciding if the matching number and disconnected matching number are equal; second: deciding if the disconnected matching number and induced matching number are equal. We show that given a bipartite graph with diameter four, deciding if the matching number and disconnected matching number are equal is NP-complete; the same holds for bipartite graphs with maximum degree three. We characterize diameter three graphs with equal matching number and disconnected matching number, which yields a polynomial time recognition algorithm. Afterwards, we show that deciding if the induced and disconnected matching numbers are equal is co-NP-complete for bipartite graphs of diameter 3. When the induced matching number is large enough compared to the maximum degree, we characterize graphs where these parameters are equal, which results in a polynomial time algorithm for bounded degree graphs.

如果饱和顶点诱导出一个不连通的子图，则称匹配是不连通的；如果饱和顶点诱导出一个1正则图，则称匹配是诱导的。断开匹配数和诱导匹配数分别定义为此类匹配的最大基数，并且已知NP-hard难以计算。本文研究了这两个参数与匹配数之间的关系。特别地，我们讨论了两个决策问题的复杂性；首先：判断匹配数与断开匹配数是否相等；第二：判断断开匹配数与诱导匹配数是否相等。我们证明了给定一个直径为4的二部图，判断匹配数和不连通匹配数是否相等是np完全的；对于最大次为3的二部图也是如此。我们描述了具有相等匹配数和断开匹配数的直径三图，得到了一个多项式时间识别算法。然后，我们证明了对于直径为3的二部图判定诱导匹配数和断开匹配数是否相等是共np完全的。当诱导匹配数与最大度相比足够大时，我们对这些参数相等的图进行表征，从而得到有界度图的多项式时间算法。

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引用次数: 0

Automata for the commutative closure of regular languages 正则语言交换闭包的自动机

IF 0.9 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences

Pub Date : 2026-01-22 DOI: 10.1016/j.jcss.2026.103762

Verónica Becher, Simón Lew Deveali, Ignacio Mollo Cunningham

Consider

A^{⁎}

, the free monoid generated by the finite alphabet A with the concatenation operation. Two words have the same commutative image when one is a permutation of the symbols of the other. The commutative closure of a language

L \subseteq A^{⁎}

is the set

C (L) \subseteq A^{⁎}

of words whose commutative image coincides with that of some word in L. We provide an algorithm that, given a regular language L, constructs a finite state automaton that accepts the commutative closure

C (L)

, in all the cases where

C (L)

regular. The problem of deciding whether

C (L)

is regular was solved by Ginsburg and Spanier in 1966 using the decidability of Presburger sentences, and by Gohon in 1985 via formal power series. Some recent work constructs the finite state automaton accepting the commutative closure of permutation languages; however, to date there had been no general algorithm that handles all the cases where

C (L)

is regular. This algorithm is the main contribution of this work.

考虑A *，由有限字母A通过连接操作生成的自由单oid。当一个词是另一个词的符号的排列时，两个词具有相同的交换象。语言L的可交换闭包为与L中的某个词的可交换象重合的词的集合C(L)。我们提供了一种算法，给定正则语言L，在C(L)正则的所有情况下，构造一个接受可交换闭包C(L)的有限状态自动机。决定C(L)是否正则的问题由Ginsburg和Spanier于1966年利用Presburger句子的可决性解决，由Gohon于1985年通过形式幂级数解决。最近的一些工作构造了接受置换语言交换闭包的有限状态自动机；然而，到目前为止，还没有一种通用的算法可以处理C(L)是正则的所有情况。该算法是本工作的主要贡献。

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引用次数: 0

Kernelization for orthogonality dimension 正交维数的核化

IF 0.9 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences

Pub Date : 2026-01-08 DOI: 10.1016/j.jcss.2026.103757

Ishay Haviv, Dror Rabinovich

The orthogonality dimension of a graph over

R

is the smallest integer d for which one can assign to every vertex a nonzero vector in

R^{d}

such that every two adjacent vertices receive orthogonal vectors. For an integer d, the

problem asks to decide whether the orthogonality dimension of a given graph over

R

is at most d. We prove that for every integer

d \geq 3

, the

problem parameterized by the vertex cover number k admits a kernel with

O (k^{d - 1})

vertices and bit-size

O (k^{d - 1} \cdot \log k)

. We complement this result by a nearly matching lower bound, showing that for any

ε > 0

, the problem admits no kernel of bit-size

O (k^{d - 1 - ε})

unless

NP \subseteq coNP / poly

. We further study the kernelizability of orthogonality dimension problems in additional settings, including over general fields and under various structural parameterizations.

R上的图的正交维数是最小的整数d，可以为每个顶点分配一个Rd中的非零向量，使得每个相邻的两个顶点都得到正交向量。对于整数d，该问题要求确定给定图在R上的正交维数是否最大为d。我们证明了对于每一个整数d≥3，用顶点覆盖数k参数化的问题承认一个具有O（kd−1）个顶点和O（kd−1⋅log (k)）位大小的核。我们用一个几乎匹配的下界来补充这一结果，表明对于任意ε>；0，问题不存在位大小为0 （kd−1−ε）的核，除非NP≠coNP/poly。我们进一步研究了正交维问题在其他情况下的可核化性，包括在一般域上和在各种结构参数化下。

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引用次数: 0

Quantum data structure for range minimum query 量程最小查询的量子数据结构

IF 0.9 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences

Pub Date : 2026-01-08 DOI: 10.1016/j.jcss.2026.103756

Qisheng Wang , Zhean Xu , Zhicheng Zhang

Given an array

a [1 . . n]

, the Range Minimum Query (RMQ) problem is to maintain a data structure that supports RMQ queries: given a range

[l, r]

, find the index of the minimum element among

a [l . . r]

, i.e.,

{arg min}_{i \in [l, r]} a [i]

. In this paper, we propose a quantum data structure that supports RMQ queries and range updates, with an optimal time complexity

\tilde{Θ} (\sqrt{n q})

for performing

q = O (n)

operations without preprocessing, compared to the classical

\tilde{Θ} (n + q)

.¹ As an application, we obtain a time-efficient quantum algorithm for k-minimum finding without the use of quantum random access memory.

给定数组a[1..]n]，范围最小查询（RMQ）问题是维护一个支持RMQ查询的数据结构：给定一个范围[l，r]，找到a[l，r]中最小元素的索引。R]，即arg mini∈[l， R]a[i]。在本文中，我们提出了一种支持RMQ查询和范围更新的量子数据结构，与经典的Θ ~ (n+q).1相比，在没有预处理的情况下执行q=O(n)操作具有最佳时间复杂度Θ ~ （nq）作为一个应用，我们获得了一种不使用量子随机存取存储器的时间高效的k-最小查找量子算法。

引用次数: 0

Morphing graph drawings in the presence of point obstacles 存在点障碍物时的变形图形绘制

IF 0.9 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences

Pub Date : 2026-01-07 DOI: 10.1016/j.jcss.2026.103755

Oksana Firman, Tim Hegemann, Boris Klemz, Felix Klesen, Marie Diana Sieper, Alexander Wolff, Johannes Zink

A crossing-free morph is a continuous deformation between two graph drawings that preserves straight-line pairwise noncrossing edges. Motivated by applications in 3D morphing problems, we initiate the study of morphing graph drawings in the plane in the presence of stationary point obstacles, which need to be avoided throughout the deformation. As our main result, we prove that it is NP-hard to decide whether such an obstacle-avoiding 2D morph between two given drawings of the same graph exists. In fact, this statement remains true even in the severely restricted special case where only three vertices have to change positions. This is in sharp contrast to the classical case without obstacles, where there is an efficiently verifiable (necessary and sufficient) criterion for the existence of a morph. Further, we provide several combinatorial results related to conditions under which the existence of a morph between two drawings of a graph can or cannot be prevented by the placement of a given number of point obstacles.

无交叉变形是两个图形之间的连续变形，它保留直线成对的不相交边。受三维变形问题应用的启发，我们开始研究平面上存在静止点障碍物的变形图形绘制，这些障碍物在整个变形过程中都需要避免。作为我们的主要结果，我们证明了在同一图的两个给定图形之间是否存在这样的避障二维变形是np困难的。事实上，即使在只有三个顶点需要改变位置的严格限制的特殊情况下，这个说法仍然成立。这与没有障碍的经典情况形成鲜明对比，在经典情况下，对于变形的存在有一个有效可验证的（必要和充分的）标准。此外，我们提供了几个组合结果，在这些条件下，图形的两个绘图之间的变形存在是否可以通过放置给定数量的点障碍物来阻止。

引用次数: 0

Quantum and classical query complexities for determining connectedness of matroids 确定拟阵连通性的量子和经典查询复杂性

IF 0.9 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences

Pub Date : 2026-01-07 DOI: 10.1016/j.jcss.2026.103758

Xiaowei Huang , Shiguang Feng , Lvzhou Li

Connectivity is a fundamental structural property of matroids, and has been studied algorithmically over 50 years. In 1974, Cunningham proposed a deterministic algorithm consuming

O (n^{2})

queries to the independence oracle to determine whether a matroid is connected. Since then, no algorithm, not even a random one, has worked better. To the best of our knowledge, the classical query complexity lower bound and the quantum complexity for this problem have not been considered. Thus, in this paper we are devoted to addressing these issues, and our contributions are threefold as follows: (i) First, we prove that the randomized query complexity of determining whether a matroid is connected is

Ω (n^{2})

and thus the algorithm proposed by Cunningham is optimal in classical computing. (ii) Second, we present a quantum algorithm with

O (n^{3 / 2})

queries, which exhibits provable quantum speedups over classical ones. (iii) Third, we prove that any quantum algorithm requires

Ω (n)

queries, which indicates that quantum algorithms can achieve at most a quadratic speedup over classical ones. Therefore, we have a relatively comprehensive understanding of the potential of quantum computing in determining the connectedness of matroids.

连通性是拟阵的基本结构性质，已经被算法研究了50多年。1974年，Cunningham提出了一种确定性算法，该算法需要对独立oracle进行O（n2）次查询来确定一个矩阵是否连通。从那时起，没有任何一种算法，甚至是随机算法，比它更有效。据我们所知，该问题的经典查询复杂度下界和量子复杂度尚未被考虑。因此，在本文中，我们致力于解决这些问题，我们的贡献如下：(i)首先，我们证明了确定一个矩阵是否连通的随机查询复杂度为Ω（n2），因此Cunningham提出的算法在经典计算中是最优的。（ii）其次，我们提出了一个具有O（n3/2）个查询的量子算法，它比经典算法具有可证明的量子加速。（iii）第三，我们证明了任何量子算法都需要Ω(n)次查询，这表明量子算法最多可以达到经典算法的二次加速。因此，我们对量子计算在确定拟阵连通性方面的潜力有了相对全面的了解。

{"title":"Quantum and classical query complexities for determining connectedness of matroids","authors":"Xiaowei Huang , Shiguang Feng , Lvzhou Li","doi":"10.1016/j.jcss.2026.103758","DOIUrl":"10.1016/j.jcss.2026.103758","url":null,"abstract":"<div><div>Connectivity is a fundamental structural property of matroids, and has been studied algorithmically over 50 years. In 1974, Cunningham proposed a deterministic algorithm consuming <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> queries to the independence oracle to determine whether a matroid is connected. Since then, no algorithm, not even a random one, has worked better. To the best of our knowledge, the classical query complexity lower bound and the quantum complexity for this problem have not been considered. Thus, in this paper we are devoted to addressing these issues, and our contributions are threefold as follows: (i) First, we prove that the randomized query complexity of determining whether a matroid is connected is <span><math><mi>Ω</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> and thus the algorithm proposed by Cunningham is optimal in classical computing. (ii) Second, we present a quantum algorithm with <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>)</mo></math></span> queries, which exhibits provable quantum speedups over classical ones. (iii) Third, we prove that any quantum algorithm requires <span><math><mi>Ω</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> queries, which indicates that quantum algorithms can achieve at most a quadratic speedup over classical ones. Therefore, we have a relatively comprehensive understanding of the potential of quantum computing in determining the connectedness of matroids.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"157 ","pages":"Article 103758"},"PeriodicalIF":0.9,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976511","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}

引用次数: 0

On the structure of Hamiltonian graphs with small independence number 小独立数哈密顿图的结构

IF 0.9 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences

Pub Date : 2026-01-05 DOI: 10.1016/j.jcss.2025.103754

Nikola Jedličková , Jan Kratochvíl

A Hamiltonian path (cycle) in a graph is a path (cycle, respectively) which passes through all of its vertices exactly once. The problems of deciding the existence of a Hamiltonian path and a Hamiltonian cycle in an input graph (called Hamiltonian Path resp. Hamiltonian Cycle) is well known to be NP-complete, and restricted classes of graphs which allow for their polynomial-time solutions are intensively investigated. Until very recently, the complexity was open even for graphs of independence number at most 3. Fomin, Golovach, Sagunov, and Simonov [arxiv 2024] showed that for every integer k, Hamiltonian Path and Hamiltonian Cycle are polynomial-time solvable in graphs of independence number bounded by k, and moreover, that these problems are in FPT when parameterized by the independence number of the input graph. As a companion structural result to these general algorithms, we determine explicit obstacles to the existence of a Hamiltonian path for small values of k, namely for graphs of independence number 2, 3, and 4. Identifying these obstacles in an input graph yields alternative polynomial-time algorithms for Hamiltonian Path and Hamiltonian Cycle with no large hidden multiplicative constants.

图中的哈密顿路径（循环）是经过所有顶点一次的路径（循环）。确定输入图中哈密顿路径和哈密顿循环是否存在的问题（称为哈密顿路径问题）。哈密顿循环)众所周知是np完全的，并且对允许其多项式时间解的图的限制类进行了深入的研究。直到最近，即使独立数最多为3的图的复杂性也是开放的。Fomin, Golovach, Sagunov， and Simonov [arxiv 2024]证明了对于每一个整数k， hamilton Path和hamilton Cycle在以k为界的独立数的图中都是多项式时间可解的，并且当用输入图的独立数参数化时，这些问题在FPT中。作为这些一般算法的伴随结构结果，我们确定了小k值的哈密顿路径存在的显式障碍，即独立数为2、3和4的图。在输入图中识别这些障碍，可以产生哈密顿路径和哈密顿循环的替代多项式时间算法，没有大的隐藏乘法常数。

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引用次数: 0

Routing few robots in a crowded network 在拥挤的网络中路由几个机器人

IF 0.9 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences

Pub Date : 2026-01-02 DOI: 10.1016/j.jcss.2025.103753

Argyrios Deligkas , Eduard Eiben , Robert Ganian , Iyad Kanj , Dominik Leko , M.S. Ramanujan

In Graph Coordinated Motion Planning, we are given a graph G some of whose vertices are occupied by robots, and we are asked to route k marked robots to their destinations while avoiding collisions and without exceeding a given budget ℓ on the number of robot moves. We continue the recent investigation of the problem [ICALP 2024], focusing on the parameter k that captures the task of routing a small number of robots in a possibly crowded graph. We prove that the problem is W[1]-hard parameterized by ℓ even for

k = 1

, but fixed-parameter tractable parameterized by k plus the treedepth of G. We complement the latter algorithm with an NP-hardness reduction which shows that both parameters are necessary to achieve tractability.

在图协调运动规划中，我们给出一个图G，其中一些顶点被机器人占据，我们被要求将k个标记的机器人路由到目的地，同时避免碰撞，并且不超过机器人移动次数的给定预算。我们继续最近对这个问题的调查[ICALP 2024]，重点关注参数k，它捕获了在可能拥挤的图中路由少量机器人的任务。我们证明了即使对于k=1，问题是W[1]-hard参数化的，但问题是固定参数可处理的，参数化是k加上树深g。我们用np -硬度约简来补充后一种算法，这表明两个参数都是实现可处理性所必需的。

引用次数: 0

The Normal Domination Game in graphs 正常统治游戏的图表

IF 0.9 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences

Pub Date : 2025-12-17 DOI: 10.1016/j.jcss.2025.103751

João Marcos Brito , Thiago Marcilon , Nicolas A. Martins , Rudini Sampaio

In 2010, Brešar, Klavžar and Rall introduced the optimization variant of the graph domination game and the game domination number. This variant has been extensively investigated in the literature, with several papers published on this topic. Interestingly, the most common variant of combinatorial games, the normal variant, in which the last to play wins, had never been investigated for the graph domination game. In this paper, we start the study of the normal play of the domination game, which we call Normal Domination Game. We first prove that this game is PSPACE-complete even in graphs with diameter two. We also use the Sprague-Grundy theory to prove that Alice (the first player) wins in the path

P_{n}

if and only if n is not a multiple of 4, and wins in the cycle

C_{n}

if and only if

n = 4 k + 3

for some integer k. Moreover, we obtain a polynomial time algorithm to decide the winner for any disjoint union of paths and cycles in the Normal Domination Game and its natural partizan variant. Finally, we also prove that the Misère Domination Game (the last to play loses) is PSPACE-complete, as are the natural partizan variants of the normal game and the misère game.

2010年Brešar、Klavžar和Rall引入了图形统治游戏的优化变体和游戏统治数。这种变体在文献中被广泛研究，有几篇论文发表在这个主题上。有趣的是，组合游戏最常见的变体，即最后一个玩家获胜的正常变体，从未被用于图形控制游戏的研究。本文开始研究统治博弈的正常博弈，我们称之为正常统治博弈。我们首先证明了这个对策即使在直径为2的图上也是pspace完全的。我们还使用Sprague-Grundy理论证明了Alice（第一个玩家）当且仅当n不是4的倍数时在路径Pn中获胜，并且当且仅当n=4k+3时在某个整数k中在循环Cn中获胜。此外，我们获得了一个多项式时间算法来确定正常统治博弈及其自然党派变种中任何路径和循环的不交并的赢家。最后，我们还证明了mis统治游戏（最后玩的人输）是pspace完全的，就像正常游戏和mis游戏的自然游击变体一样。

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引用次数: 0

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