Journal of Computer and System Sciences最新文献_第4页

On the structural parameterized complexity of defective coloring 缺陷着色的结构参数化复杂度

IF 0.9 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences

Pub Date : 2025-11-11 DOI: 10.1016/j.jcss.2025.103736

Sriram Bhyravarapu , Pankaj Kumar , Saket Saurabh

In this paper, we consider the problem Defective Coloring. Given a graph G and two positive integers k and

Δ^{⁎}

, the objective is to determine whether it is possible to obtain a coloring (not necessarily proper) of the vertices of G using at most k colors such that each vertex has at most

Δ^{⁎}

neighbors in the same color class. Defective Coloring is a generalization of Graph Coloring with

Δ^{⁎} = 0

. The optimization variant of this problem, which aims to find the minimum number of colors k, is known to be NP-hard even for split graphs and cographs. Belmonte, Lampis, and Mitsou (SIDMA 2020) showed that Defective Coloring is W[1]-hard when parameterized by feedback vertex set or by treedepth, which implies W[1]-hardness for path-width and treewidth parameters. The problem is W[1]-hard parameterized by modular-width or clique-width as Defective Coloring is NP-hard on cographs. They asked whether Defective Coloring is fixed-parameter tractable (FPT) when parameterized by modular-width, neighborhood diversity or clique-width combined with either k or

Δ^{⁎}

. In an effort to address the question concerning modular-width, this study investigates the parameters neighborhood diversity and twin-cover, which are special cases of modular-width. We show that Defective Coloring is FPT when parameterized by twin-cover, distance to disjoint paths, or the combined parameters neighborhood diversity and k. The latter implies an FPT algorithm for complete-d-partite graphs, a subclass of cographs, parameterized by d. We present an algorithm for graphs with bounded distance to d-degree. We also present a 1-additive approximation algorithm for split graphs.

本文考虑了缺陷着色问题。给定一个图G和两个正整数k和Δ ，目标是确定是否有可能使用最多k种颜色获得G的顶点的着色（不一定是适当的），使得每个顶点在同一颜色类中最多有Δ 邻居。缺陷着色是Δ =0的图着色的一种推广。这个问题的优化变体，旨在找到最小颜色k的数量，已知即使对于分割图和图也是np困难的。Belmonte, Lampis, and Mitsou （SIDMA 2020）表明，当用反馈顶点集或树深度参数化时，缺陷着色是W[1]-硬度，这意味着路径宽度和树宽度参数的硬度为W[1]-硬度。由于缺陷着色在图上是NP-hard的，所以问题是用模宽度或团宽度参数化w[1]-hard。他们问，当用模块宽度、邻域多样性或与k或Δ联合的团宽度进行参数化时，缺陷着色是否是固定参数可处理的（FPT）。为了解决模块宽度的问题，本文研究了模块宽度的特殊情况——邻域多样性和双覆盖参数。我们证明了当用双覆盖、到不相交路径的距离或结合参数邻域多样性和k来参数化时，缺陷着色是FPT。后者暗示了一种用于完全d部图的FPT算法，完全d部图是图的一个子类，参数化为d。我们提出了一种用于到d度有界距离的图的算法。我们还提出了一个分割图的1加性近似算法。

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引用次数: 0

Algorithms and hardness results for the (k,ℓ)-cover problem （k, r）-覆盖问题的算法和硬度结果

IF 0.9 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences

Pub Date : 2025-11-03 DOI: 10.1016/j.jcss.2025.103727

Amirali Madani , Anil Maheshwari , Babak Miraftab , Bodhayan Roy

A connected graph has a

(k, ℓ)

-cover if each of its edges is contained in at least ℓ cliques of order k. Motivated by recent advances in extremal combinatorics and the literature on edge modification problems, we study the algorithmic version of the

(k, ℓ)

-cover problem. Given a connected graph G, the

(k, ℓ)

-cover problem is to identify the smallest subset of non-edges of G such that their addition to G results in a graph with a

(k, ℓ)

-cover. For every constant

k \geq 3

, we show that the

(k, 1)

-cover problem is

NP

-complete for general graphs. Moreover, we show that for every constant

k \geq 3

, the

(k, 1)

-cover problem admits no polynomial-time constant-factor approximation algorithm unless

P = NP

. However, we show that the

(3, 1)

-cover problem can be solved in polynomial time when the input graph is chordal. For the class of trees and general values of k, we show that the

(k, 1)

-cover problem is

NP

-hard even for spiders. However, we show that for every

k \geq 4

, the

(3, k - 2)

-cover and the

(k, 1)

-cover problems are constant-factor approximable when the input graph is a tree.

如果连通图的每条边都包含在至少r个k阶的团中，则连通图具有(k, r)-覆盖。受极值组合学的最新进展和边修正问题的文献的启发，我们研究了(k, r)-覆盖问题的算法版本。给定一个连通图G， (k, r)-覆盖问题是识别G的非边的最小子集，使得它们加到G上得到一个具有(k, r)-覆盖的图。对于每一个常数k≥3，我们证明(k,1)-覆盖问题对于一般图是np完全的。此外，我们证明了对于每一个常数k≥3，(k,1)-覆盖问题不允许多项式时间常数因子逼近算法，除非P=NP。然而，我们证明了当输入图是弦图时，(3,1)-覆盖问题可以在多项式时间内解决。对于树类和k的一般值，我们证明(k,1)-覆盖问题即使对于蜘蛛也是np困难的。然而，我们证明了对于每k≥4，当输入图是树时，(3,k−2)-覆盖问题和(k,1)-覆盖问题是常数因子近似的。

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引用次数: 0

Redundancy of information: Lowering effective dimension 信息冗余：降低有效维数

IF 0.9 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences

Pub Date : 2025-11-03 DOI: 10.1016/j.jcss.2025.103732

Jun Le Goh , Joseph S. Miller , Mariya I. Soskova , Linda Westrick

Let

A_{t} \subseteq 2^{ω}

denote the set of infinite sequences of effective dimension t. Greenberg, Miller, Shen, and Westrick [6] studied both how near and how far an infinite sequence of dimension s can be from the closest sequence of dimension t, where distance in

2^{ω}

is measured using the Besicovitch pseudometric. They found

\inf_{X \in A_{s}} d (X, A_{t})

and

\sup_{X \in A_{s}} d (X, A_{t})

for all

s, t \in [0, 1]

, except for the supremum when

t < s < 1

. This case is made difficult by the fact that the information in a dimension s sequence can be coded redundantly, so it is not clear what density of changes is needed to erase enough of that information. We completely solve the dimension reduction problem. We also identify classes of sequences for which these infima and suprema are realized as minima and maxima. When

t < s

, we find

d (X, A_{t})

is minimized when X is a Bernoulli

H^{- 1} (s)

-random, and maximized when X belongs to a class of infinite sequences that we call s-codewords. When

s < t

, the situation is reversed. Finally, we prove that all distances between the extrema are realized.

设At≤2ω，表示有效维数为t的无限序列的集合。Greenberg、Miller、Shen和Westrick[6]研究了一个维数为s的无限序列与最近维数为t的序列之间的距离有多近和多远，其中2ω中的距离使用Besicovitch伪度量来测量。他们发现对于所有s，t∈[0,1]，除了t<；s<；1时的极值外，infX∈As d（X,At）和supX∈As d（X,At）。由于维度序列中的信息可以被冗余编码，因此不清楚需要多大的更改密度才能擦除足够的信息，这使得这种情况变得困难。我们完全解决了降维问题。我们还确定了这些无穷值和上值被实现为极小值和极大值的序列的类别。当t<；s时，我们发现当X是伯努利H−1(s)随机时，d（X,At）是最小的，当X属于一类我们称为s码字的无限序列时，d（X,At）是最大的。当s<；t时，情况正好相反。最后，我们证明了所有极值之间的距离都是可以实现的。

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引用次数: 0

Decomposing finite-valued two-way finite transducers 分解有限值双向有限换能器

IF 0.9 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences

Pub Date : 2025-10-31 DOI: 10.1016/j.jcss.2025.103731

Hsu-Chun Yen , Di-De Yen

Finite transducers are finite automata with outputs. A transducer is finite-valued if the number of different outputs for any input string is bounded by a constant, and is single-valued if the constant is one. It is known that finite-valued one-way finite transducers enjoy a nice property that they can be decomposed into finitely many single-valued ones. In this paper, we develop an analytical technique for finite-valued 2-way finite transducers, capable of not only showing the decomposability result but also revealing the decomposition complexity. In particular, we show that every finite-valued two-way finite transducer can be effectively decomposed into a finite collection of single-valued two-way finite transducers. The number of such single-valued transducers is bounded by a tower of three exponentials in the size of the original transducer, while the size of each single-valued transducer is bounded by a tower of five exponentials. For special classes of 2-way transducers such as sweeping transducers and reversal-bounded transducers, lower decomposition complexity can be achieved by simplifying certain steps in the decomposition procedure. Finally, our decomposition analysis also allows us to derive complexity bounds for the equivalence problem for various classes of finite-valued 2-way finite transducers.

有限换能器是具有输出的有限自动机。如果任何输入字符串的不同输出的数量由一个常数限定，则换能器是有限值的，如果该常数为1，则换能器是单值的。已知有限值单向有限换能器具有可以分解为有限多个单值换能器的优良性质。在本文中，我们开发了一种有限值双向有限传感器的解析技术，它不仅能够显示分解结果，而且能够显示分解的复杂性。特别地，我们证明了每个有限值双向有限换能器都可以有效地分解为单值双向有限换能器的有限集合。这种单值换能器的数量由原始换能器大小的三个指数塔限制，而每个单值换能器的大小由五个指数塔限制。对于特殊类型的双向换能器，如扫描换能器和反向有界换能器，可以通过简化分解过程中的某些步骤来降低分解复杂度。最后，我们的分解分析还使我们能够推导出各种有限值双向有限换能器等效问题的复杂性界限。

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引用次数: 0

Search-space reduction via essential vertices revisited: Vertex multicut and cograph deletion 通过重访基本顶点来减少搜索空间：顶点多切割和图形删除

IF 0.9 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences

Pub Date : 2025-10-30 DOI: 10.1016/j.jcss.2025.103730

Bart M.P. Jansen , Ruben F.A. Verhaegh

For an optimization problem Π on graphs whose solutions are vertex sets, a vertex v is called c-essential for Π if all solutions of size at most

contain v. Recent work showed that polynomial-time algorithms to detect c-essential vertices can be used to reduce the search-space of fixed-parameter tractable algorithms solving such problems parameterized by the size k of the solution. We provide several new upper- and lower bounds for detecting essential vertices. For example, we give a polynomial-time algorithm for 3-Essential detection for Vertex Multicut, which translates into an algorithm that finds a minimum multicut of an undirected n-vertex graph G in time

2^{O (ℓ^{3})} \cdot n^{O (1)}

, where ℓ is the number of vertices in an optimal solution that are not 3-essential. Our positive results are obtained by analyzing the integrality gaps of certain linear programs. Our lower bounds show that for sufficiently small values of c, the detection task becomes NP-hard assuming the Unique Games Conjecture. For example, we show that (

2 - ε

)-Essential detection for Directed Feedback Vertex Set is NP-hard under this conjecture, thereby proving that the existing algorithm that detects 2-essential vertices is best-possible.

对于解为顶点集的图上的优化问题Π，如果所有大小的解最多包含v，则顶点v称为Π的c-必要顶点。最近的工作表明，检测c-必要顶点的多项式时间算法可以用来减少求解由解的大小k参数化的固定参数可处理算法的搜索空间。我们提供了几个新的检测基本顶点的上界和下界。例如，我们给出了一个顶点多切的3-必要检测的多项式时间算法，它转化为一个在时间为2O(l3)⋅nO(1)的无向n顶点图G的最小多切算法，其中，l0为最优解中非3-必要顶点的个数。通过对某些线性规划的完整性间隙的分析，得到了一些积极的结果。我们的下界表明，对于足够小的c值，假设唯一对策猜想，检测任务变得np困难。例如，我们证明了在这个猜想下有向反馈顶点集的(2−ε)-基本检测是np困难的，从而证明了现有的检测2-基本顶点的算法是最好的。

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引用次数: 0

Bringing memory to Boolean networks: A unifying framework 将内存引入布尔网络：一个统一的框架

IF 0.9 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences

Pub Date : 2025-10-30 DOI: 10.1016/j.jcss.2025.103729

Maximilien Gadouleau , Loïc Paulevé , Sara Riva

Boolean networks are extensively applied as models of complex dynamical systems, aiming at capturing essential features related to causality and synchronicity of the state changes of components along time. Dynamics of Boolean networks result from the application of their Boolean map according to a so-called update mode, specifying the possible transitions between network configurations. In this paper, we explore update modes that possess a memory on past configurations, and provide a generic framework to define them. We show that recently introduced modes such as the most permissive and interval modes can be naturally expressed in this framework, and we propose novel update modes, the history-based, trapping, and subcube-based modes. Building on the unified definitions, we provide a comprehensive comparison of memory-based update modes, resulting in their hierarchy by simulation and weak simulation. Finally, we highlight consequences of introducing memory on the notions of trajectory and attractors.

布尔网络作为复杂动力系统的模型被广泛应用，其目的是捕捉部件状态随时间变化的因果性和同步性等本质特征。布尔网络的动态是根据所谓的更新模式应用其布尔映射而产生的，该模式指定了网络配置之间可能的转换。在本文中，我们探索了具有过去配置记忆的更新模式，并提供了一个通用框架来定义它们。我们证明了最近引入的模式，如最允许模式和间隔模式，可以在这个框架中自然地表达，我们提出了新的更新模式，基于历史的，捕获的，和基于子立方体的模式。在统一定义的基础上，我们对基于内存的更新模式进行了全面的比较，得出了基于仿真和弱仿真的层次结构。最后，我们强调了引入记忆对轨迹和吸引子概念的影响。

引用次数: 0

The complexity of (Pk,Pℓ)-arrowing （Pk, p0）的复杂度

IF 0.9 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences

Pub Date : 2025-10-29 DOI: 10.1016/j.jcss.2025.103726

Zohair Raza Hassan, Edith Hemaspaandra, Stanisław Radziszowski

For fixed nonnegative integers k and ℓ, the

(P_{k}, P_{ℓ})

-Arrowing problem asks whether a given graph, G, has a red/blue coloring of

E (G)

such that there are no red copies of

P_{k}

and no blue copies of

P_{ℓ}

. The problem is trivial when

\max (k, ℓ) \leq 3

, but has been shown to be coNP-complete when

k = ℓ = 4

. In this work, we show that the problem remains coNP-complete for all pairs of k and ℓ, except

(3, 4)

, and when

\max (k, ℓ) \leq 3

. We define and prove the existence of special graphs that we call “transmitters.” Using transmitters, we construct gadgets for three distinct cases: 1)

k = 3

and

ℓ \geq 5

, 2)

ℓ > k \geq 4

, and 3)

ℓ = k \geq 4

. For

(P_{3}, P_{4})

-Arrowing we show a polynomial-time algorithm by reducing the problem to 2SAT, thus successfully categorizing the complexity of all

(P_{k}, P_{ℓ})

-Arrowing problems.

对于固定的非负整数k和r，（Pk，P, r）箭头问题问的是给定的图G，是否具有E(G)的红/蓝着色，使得P， r没有红色的副本，P， r没有蓝色的副本。当max (k, r)≤3时，问题是平凡的，但当k= r =4时，问题是conp完备的。在这项工作中，我们证明了除（3,4）外，当max (k, r)≤3时，对于k和r的所有对，问题保持conp完全。我们定义并证明了我们称之为“传送”的特殊图的存在性。利用变送器，我们构造了三种不同情况下的小波：1)k=3且r≥5,2)r >k≥4,3)r =k≥4。对于(P3,P4)- arrow问题，我们展示了一个多项式时间算法，通过将问题简化为2SAT，从而成功地对所有（Pk，P, r）- arrow问题的复杂性进行了分类。

引用次数: 0

Computational complexity of covering multigraphs with semi-edges: Small cases 用半边覆盖多图的计算复杂度：小情况

IF 0.9 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences

Pub Date : 2025-10-17 DOI: 10.1016/j.jcss.2025.103714

Jan Bok , Jiří Fiala , Petr Hliněný , Nikola Jedličková , Jan Kratochvíl

We initiate the study of computational complexity of graph coverings, aka locally bijective graph homomorphisms, for graphs with semi-edges. The notion of graph covering is a discretization of coverings between surfaces or topological spaces, a notion well known and deeply studied in classical topology. Graph covers have found applications in discrete mathematics for constructing highly symmetric graphs, and in computer science in the theory of local computations. In 1991, Abello, Fellows, and Stillwell asked for a classification of the computational complexity of deciding if an input graph covers a fixed target graph, in the ordinary setting (of graphs with only edges). Although many general results are known, the full classification is still open. In spite of that, we propose to study the more general case of covering graphs composed of normal edges (including multiedges and loops) and so-called semi-edges. Semi-edges are becoming increasingly popular in modern topological graph theory, as well as in mathematical physics. They also naturally occur in the local computation setting, since they are lifted to matchings in the covering graph. We show that the presence of semi-edges makes the covering problem considerably harder; e.g., it is no longer sufficient to specify the vertex mapping induced by the covering, but one necessarily has to deal with the edge mapping as well. We show some solvable cases and, in particular, completely characterize the complexity of the already very nontrivial problem of covering one- and two-vertex (multi)graphs with semi-edges. Our NP-hardness results are proven for simple input graphs, and in the case of regular two-vertex target graphs, even for bipartite ones. We remark that our new characterization results also strengthen previously known results for covering graphs without semi-edges, and they in turn apply to an infinite class of simple target graphs with at most two vertices of degree more than two. Some of the results are moreover proven in a more general setting (e.g., finding k-tuples of pairwise disjoint perfect matchings in regular graphs).

我们开始了图覆盖的计算复杂度的研究，又称局部双射图同态，对于具有半边的图。图覆盖的概念是曲面或拓扑空间之间的覆盖的离散化，这是一个在经典拓扑学中众所周知并被深入研究的概念。图盖在离散数学中用于构造高度对称的图，在计算机科学的局部计算理论中也有应用。1991年，Abello， Fellows和Stillwell要求对在普通设置（只有边的图）中决定输入图是否覆盖固定目标图的计算复杂度进行分类。虽然许多一般的结果是已知的，但完整的分类仍然是开放的。尽管如此，我们建议研究由正规边（包括多边和环）和所谓的半边组成的覆盖图的更一般的情况。半边在现代拓扑图理论和数学物理中越来越流行。它们也自然地出现在局部计算设置中，因为它们被提升到覆盖图中的匹配。我们证明了半边的存在使覆盖问题变得相当困难；例如，指定由覆盖引起的顶点映射已经不够了，还必须处理边缘映射。我们展示了一些可解的情况，特别是，完全表征了用半边覆盖单顶点和双顶点（多）图这个已经非常重要的问题的复杂性。我们的np -硬度结果证明了简单的输入图，在规则的两顶点目标图的情况下，甚至对于二部图。我们注意到，我们的新表征结果也加强了先前已知的无半边覆盖图的结果，并且它们反过来适用于无限类的简单目标图，其中最多有两个顶点的次数大于2。一些结果还在更一般的情况下得到了证明（例如，在正则图中找到成对不相交完美匹配的k元组）。

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引用次数: 0

Exploration of graphs with excluded minors 排除小调图的探索

IF 0.9 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences

Pub Date : 2025-10-10 DOI: 10.1016/j.jcss.2025.103725

Júlia Baligács, Yann Disser, Irene Heinrich, Pascal Schweitzer

We study the online graph exploration problem proposed by Kalyanasundaram and Pruhs (1994) and prove a constant competitive ratio on minor-free graphs. This result encompasses and significantly extends the graph classes that were previously known to admit a constant competitive ratio. The main ingredient of our proof is that we find a connection between the performance of the particular exploration algorithm

and the existence of light spanners. Conversely, we exploit this connection to construct light spanners of bounded genus graphs. In particular, we achieve a lightness that improves on the best known upper bound for genus

g \geq 1

and recovers the known tight bound for the planar case (

g = 0

).

我们研究了Kalyanasundaram和Pruhs（1994）提出的在线图探索问题，并证明了无次图上的恒定竞争比。这个结果包含并显著扩展了以前已知的具有恒定竞争比的图类。我们证明的主要成分是，我们发现了特定探索算法的性能与光扳手的存在之间的联系。反过来，我们利用这个联系来构造有界属图的轻扳手。特别是，我们实现了一种轻度，它改进了已知的g≥1属的上界，并恢复了平面情况（g=0）的已知紧界。

引用次数: 0

Dynamic programming on bipartite tree decompositions 二部树分解的动态规划

IF 0.9 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences

Pub Date : 2025-10-09 DOI: 10.1016/j.jcss.2025.103722

Lars Jaffke , Laure Morelle , Ignasi Sau , Dimitrios M. Thilikos

We revisit a graph width parameter that we dub bipartite treewidth (btw). Bipartite treewidth can be seen as a common generalization of treewidth and the odd cycle transversal number, and is closely related to odd-minors. Intuitively, a bipartite tree decomposition is a tree decomposition whose bags induce almost bipartite graphs and whose adhesions contain at most one “bipartite” vertex, while the width of such decomposition measures the number of “non-bipartite” vertices in a bag. We provide para-NP-completeness results and develop dynamic programming techniques to solve problems on graphs of small btw. In particular, we show that

K_{t}

-Subgraph-Cover, Weighted Independent Set, Odd Cycle Transversal, and Maximum Weighted Cut are

FPT

parameterized by btw. We also provide the following dichotomy when H is a 2-connected graph: if H is bipartite, then H-{Subgraph/Induced-Subgraph/Odd-Minor/Scattered}-Packing is para-NP-complete parameterized by btw while, if H is non-bipartite, then the problem is solvable in XP-time.

我们重新审视一个图宽度参数，我们称之为二部树宽度（btw）。二部树宽度可以看作是树宽度和奇环截数的共同推广，并且与奇副数密切相关。直观地说，二部树分解是这样一种树分解，它的袋归纳出几乎二部图，它的粘连最多包含一个“二部”顶点，而这种分解的宽度度量了一个袋中“非二部”顶点的数量。我们提供了准np完备性结果，并开发了动态规划技术来解决小btw图上的问题。特别地，我们证明了Kt-Subgraph-Cover、加权独立集、奇环截线和最大加权截线是由btw参数化的FPT。当H是2连通图时，我们还给出了以下二分法：如果H是二部图，则H-{Subgraph/ inducd_subgraph /Odd-Minor/Scattered}- packing是btw参数化的准np完全，如果H是非二部图，则问题在XP-time内可解。

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引用次数: 0