Journal of Computer and System Sciences最新文献

英文中文

Making the interval membership width of temporal graphs connected and bidirectional 使时间图的区间隶属度宽度连通和双向

IF 1.1 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences

Pub Date : 2025-07-03 DOI: 10.1016/j.jcss.2025.103684

Filippos Christodoulou , Pierluigi Crescenzi , Andrea Marino , Ana Silva , Dimitrios M. Thilikos

Temporal graphs are graphs that evolve over time. Many problems which are polynomial-time solvable in standard graphs become NP-hard when appropriately defined in the realm of temporal graphs.This suggested the definition of several parameters for temporal graphs and to prove the fixed-parameter tractability of several problems with respect to these parameters. In this paper, we introduce a hierarchy of parameters based on the previously defined interval membership width and the temporal evolution of the connected components of the underlying static graph. We show that the Eulerian trail problem and the temporal 2-coloring problem are both fixed-parameter tractable with respect to any parameter in the hierarchy. We also introduce a vertex-variant of the parameters and show that the firefighter problem, known to be FPT with respect to the vertex-variant of the interval membership width, is also FPT with respect to one of the parameters in the second level of the hierarchy.

时间图是随时间变化的图。许多在标准图中多项式时间可解的问题，在时间图中适当地定义后，就变成了np困难问题。提出了时间图的几个参数的定义，并证明了几个问题相对于这些参数的定参数可跟踪性。在本文中，我们引入了一个基于先前定义的区间隶属度宽度和底层静态图的连通分量的时间演化的参数层次结构。我们证明了欧拉轨迹问题和时间2-着色问题对于层次结构中的任何参数都是固定参数可处理的。我们还引入了参数的一个顶点变量，并表明消防员问题，已知是相对于区间隶属度宽度的顶点变量的FPT，也是相对于层次结构第二层中的一个参数的FPT。

引用次数: 0

Complexity framework for forbidden subgraphs IV: The Steiner Forest problem 禁止子图的复杂度框架IV：斯坦纳森林问题

IF 1.1 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences

Pub Date : 2025-06-27 DOI: 10.1016/j.jcss.2025.103682

Hans L. Bodlaender , Matthew Johnson , Barnaby Martin , Jelle J. Oostveen , Sukanya Pandey , Daniël Paulusma , Siani Smith , Erik Jan van Leeuwen

We study Steiner Forest on H-subgraph-free graphs, that is, graphs that do not contain some fixed graph H as a (not necessarily induced) subgraph. In contrast to the related Steiner Tree problem, Steiner Forest falls outside a recent framework that completely characterizes the complexity of many problems on H-subgraph-free graphs. Hence, the complexity of Steiner Forest on H-subgraph-free graphs remained open. Our main results are four polynomial-time algorithms for different excluded graphs H that are central to further understand its complexity. We also study the complexity of Steiner Forest for graphs with a small c-deletion set, that is, a small set X of vertices such that each connected component of

G - X

has size at most c. For this parameter, we give two algorithms that we later employ as subroutines (including a faster algorithm when

c = 1

, that is, the vertex cover number) and exhibit a dichotomy theorem.

我们研究了无H子图上的斯坦纳森林，即不包含固定图H作为（不一定是诱导的）子图的图。与相关的斯坦纳树问题相比，斯坦纳森林问题不属于最近的一个框架，该框架完全表征了h-子图上许多问题的复杂性。因此，H-subgraph-free图上的Steiner Forest的复杂度是开放的。我们的主要结果是针对不同的排除图H的四种多项式时间算法，这是进一步理解其复杂性的核心。我们还研究了具有小c-删除集的图的斯坦纳森林的复杂性，即一个小的顶点集X，使得G−X的每个连接分量的大小最多为c。对于这个参数，我们给出了两种算法，我们稍后将其用作子程序（包括当c=1时更快的算法，即顶点覆盖数），并展示了二分定理。

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引用次数: 0

The edit distance to k-subsequence universality 对k-子序列通用性的编辑距离

IF 1.1 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences

Pub Date : 2025-06-16 DOI: 10.1016/j.jcss.2025.103681

Joel D. Day , Pamela Fleischmann , Maria Kosche , Tore Koß , Florin Manea , Stefan Siemer

A word u is a subsequence of another word w if u is obtained from w by deleting some of its letters. In the 1970s, Simon defined the relation

\sim_{k}

(called now Simon-Congruence) as follows: two words having the same set of subsequences of length k are

\sim_{k}

-congruent. It is thus natural to ask, for non k-equivalent words w and u, what is the minimal number of edit operations that we need to perform on w to obtain a word which is

\sim_{k}

-equivalent to u. Here, we consider this problem in a specific setting: when u is a k-subsequence universal word. A word u with

a l p h (u) = Σ

is called k-subsequence universal if the set of length-k subsequences of u contains all possible words of length k over Σ. As such, our results are a series of efficient algorithms computing the edit distance from w to the language of k-subsequence universal words.

一个单词u是另一个单词w的子序列，如果u是通过删除w中的一些字母而得到的。在20世纪70年代，Simon定义了关系~ k（现在称为Simon-同余）如下：具有相同长度为k的子序列集的两个单词是~ k同余的。因此，很自然地要问，对于非k-等价的单词w和u，我们需要对w执行多少次编辑操作才能获得一个与u - k-等价的单词。这里，我们在一个特定的设置中考虑这个问题：当u是一个k-子序列全称词时。如果u的长度为k- k的子序列集合包含了长度为k / Σ的所有可能的单词，那么一个单词u (u)=Σ被称为k-子序列全称。因此，我们的结果是一系列有效的算法，计算从w到k-子序列通用词的语言的编辑距离。

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引用次数: 0

On the parameterized complexity of lineal topologies (depth-first spanning trees) with many or few leaves 多叶或少叶线性拓扑（深度优先生成树）的参数化复杂度

IF 1.1 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences

Pub Date : 2025-05-27 DOI: 10.1016/j.jcss.2025.103680

Benjamin Bergougnoux , Nello Blaser , Michael Fellows , Petr Golovach , Frances Rosamond , Emmanuel Sam

This paper considers four problems with possible applications in network design: Given a graph G with

| G | = n

and an integer

k \geq 0

, does G have a DFS tree with (i) ≤k leaves, (ii) ≥k leaves, (iii)

\leq n - k

leaves, and (iv)

\geq n - k

leaves? We show that all four problems are NP-hard. When parameterized by k, we prove that while (i) is para-NP-hard and (ii) is W[1]-hard, both (iii) and (iv) admit polynomial kernels with

O (k^{3})

vertices, implying FPT algorithms running in

k^{O (k)} \cdot n^{O (1)}

time. Our polynomial kernels are based on a

O (k)

-sized vertex cover structure associated with the solution of these problems. As a byproduct, we obtain polynomial kernels for these problems parameterized by the vertex cover number of the input graph.

本文考虑了网络设计中可能应用的四个问题：给定一个|G|=n且整数k≥0的图G， G是否存在(i)≤k个叶子，(ii)≥k个叶子，(iii)≤n−k个叶子，(iv)≥n−k个叶子的DFS树？我们证明这四个问题都是np困难的。当用k参数化时，我们证明了(i)是para-NP-hard，（ii）是W - [1]-hard，（iii）和（iv）都承认有O（k3）个顶点的多项式核，这意味着FPT算法在kO(k)⋅nO(1)时间内运行。我们的多项式核基于与这些问题的解相关的O(k)大小的顶点覆盖结构。作为副产品，我们得到了这些问题的多项式核，这些问题由输入图的顶点覆盖数参数化。

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引用次数: 0

An FPT algorithm for timeline cover 时间线覆盖的FPT算法

IF 1.1 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences

Pub Date : 2025-05-22 DOI: 10.1016/j.jcss.2025.103679

Riccardo Dondi , Manuel Lafond

One of the most studied problem in theoretical computer science, Vertex Cover, has been recently considered in the temporal graph framework. Here we study a Vertex Cover variant, called k-TimelineCover. Given a temporal graph k-TimelineCover asks to define an interval for each vertex so that for every temporal edge existing in a timestamp t, at least one of the endpoints has an interval that includes t. The goal is to decide whether it is possible to cover every temporal edge while using vertex intervals of total span at most k. k-TimelineCover has been shown to be NP-hard, but its parameterized complexity has not been fully understood when parameterizing by the span of the solution. We settle this open problem by giving an FPT algorithm that combines two techniques, a modified form of iterative compression and a reduction to Digraph Pair Cut.

顶点覆盖是理论计算机科学中研究最多的问题之一，最近在时间图框架中得到了考虑。这里我们研究一个顶点覆盖的变体，称为k-TimelineCover。给定一个时序图k-TimelineCover要求为每个顶点定义一个间隔,这样每时间边缘存在一个时间戳t,至少有一个端点的一个区间,其中包括t。我们的目标是决定是否可以覆盖每一个时间边缘在使用顶点总跨度的间隔最多k k-TimelineCover已被证明是np困难,但其参数化的复杂性尚未完全理解当张成的空间参数化的解决方案。我们给出了一种FPT算法，该算法结合了两种技术，一种改进的迭代压缩形式和对有向图对切割的简化。

引用次数: 0

Weighted group search on the disk & improved lower bounds for priority evacuation 磁盘上的加权群搜索&改进的优先疏散下界

IF 1.1 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences

Pub Date : 2025-05-15 DOI: 10.1016/j.jcss.2025.103678

Konstantinos Georgiou, Xin Wang

We study weighted group search on a disk, where two unit-speed agents must locate a hidden target exactly distance 1 away (within a unit-radius disk), starting from the same point. Agents share findings instantly via the wireless model. The goal is to minimize the worst-case weighted average of their arrival times, with one agent weighted 1 and the other

w \in [0, 1]

. This problem extends prior work on search on a line (with known optimal strategies) and the priority evacuation problem, which corresponds to

w = 0

and still has a notable gap between upper and lower bounds. Our contributions are the following: (1) Upper bounds for all w, using refined known techniques. (2) A novel lower-bound framework using linear programming, inspired by metric embeddings, and (3) Improved bounds for priority evacuation, raising the lower bound from 4.38962 to 4.56798.

我们研究了磁盘上的加权群搜索，其中两个单位速度代理必须从同一点出发，在距离为1的距离（在单位半径的磁盘内）找到一个隐藏目标。代理们通过无线模型即时分享发现。目标是最小化它们到达时间的最坏情况加权平均值，其中一个代理的权重为1，另一个代理w∈[0,1]。该问题扩展了先前的在线搜索工作（具有已知的最优策略）和优先级疏散问题，该问题对应于w=0，并且在上界和下界之间仍然存在明显的差距。我们的贡献如下：(1)所有w的上界，使用改进的已知技术。(2)基于度量嵌入的线性规划框架；(3)改进了优先级疏散的下限，将下限从4.38962提高到4.56798。

引用次数: 0

Acyclic, star and injective colouring: A complexity picture for H-free graphs 无环、星形和内射着色：无h图的复杂度图

IF 1.1 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences

Pub Date : 2025-05-05 DOI: 10.1016/j.jcss.2025.103662

Jan Bok , Nikola Jedličková , Barnaby Martin , Pascal Ochem , Daniël Paulusma , Siani Smith

A (proper) colouring is acyclic, star, or injective if any two colour classes induce a forest, star forest or disjoint union of vertices and edges, respectively. The corresponding decision problems are Acyclic Colouring, Star Colouring and Injective Colouring. We give almost complete complexity classifications for Acyclic Colouring, Star Colouring and Injective Colouring on H-free graphs (for each of the problems, we have one open case). Moreover, we give full complexity classifications if the number of colours k is fixed, that is, not part of the input. From our study it follows that for fixed k, the three problems behave in the same way, but this is no longer true if k is part of the input. To obtain several of our results we prove stronger complexity results that in particular involve the girth of a graph and the class of line graphs of multigraphs.

如果任意两个颜色类分别诱导出一个森林、星林或顶点和边的不相交并，则一个（适当的）着色是无环、星形或内射的。相应的决策问题有无环着色、星形着色和内射着色。我们给出了H-free图上的无环着色、星形着色和内射着色的几乎完全的复杂性分类（对于每一个问题，我们都有一个开放的情况）。此外，如果颜色k的数量是固定的，也就是说，不是输入的一部分，我们给出了完整的复杂性分类。从我们的研究中可以得出，对于固定的k，这三个问题的表现是一样的，但如果k是输入的一部分，这就不再成立了。为了得到我们的几个结果，我们证明了更强的复杂性结果，特别是涉及图的周长和多图的线形图类。

引用次数: 0

State complexity of one-way quantum finite automata together with classical states 单向量子有限自动机与经典态的状态复杂性

IF 1.1 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences

Pub Date : 2025-05-02 DOI: 10.1016/j.jcss.2025.103659

Ligang Xiao , Daowen Qiu

One-way quantum finite automata together with classical states (1QFAC) proposed by Qiu et al. is a new one-way quantum finite automata (1QFA) model that integrates quantum finite automata (QFA) and deterministic finite automata (DFA). The relationshipsand balances between quantum states and classical states in 1QFAC are still not clear. In this paper, we obtain the following results: (1) We optimize the bound given by Qiu et al. that characterizes the relationships between quantum basis states and classical states as well as the equivalent minimal DFA. (2) We give an upper bound showing how many classical states are needed upon reducing the quantum basis states of 1QFAC. (3) We give a lower bound on the classical state number of 1QFAC for recognizing any given regular language, and show that the lower bound is exact if the given language is finite. (4) We show that 1QFAC are exponentially more succinct than DFA and probabilistic finite automata (PFA) for some regular languages. (5) We point out essential relationships between 1QFAC, MO-1QFA and multi-letter 1QFA, and induce a result regarding quantitative relationships between multi-letter 1QFA and DFA.

Qiu等人提出的单向量子有限自动机与经典态（1QFAC）是一种将量子有限自动机（QFA）与确定性有限自动机（DFA）相结合的新型单向量子有限自动机（1QFA）模型。1QFAC中量子态与经典态之间的关系和平衡尚不清楚。在本文中，我们得到了以下结果：(1)我们优化了Qiu等人给出的表征量子基态与经典态之间关系的界以及等效最小DFA。(2)给出了减少1QFAC量子基态所需经典态个数的上界。(3)给出了识别任意给定正则语言的1QFAC经典状态数的下界，并证明了该下界在给定语言是有限的情况下是精确的。(4)对于一些正则语言，我们证明了1QFAC比DFA和概率有限自动机（PFA）更简洁。(5)指出了1QFAC、MO-1QFA和多字母1QFA之间的本质关系，并推导出了多字母1QFA与DFA之间的定量关系。

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引用次数: 0

Compact distributed certification of geometric graph classes 几何图类的紧凑分布证明

IF 1.1 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences

Pub Date : 2025-05-02 DOI: 10.1016/j.jcss.2025.103661

Benjamin Jauregui , Pedro Montealegre , Diego Ramirez-Romero , Ivan Rapaport

Distributed proofs allow network nodes to collectively verify if the network satisfies a given predicate. The most versatile mechanism, known as a proof labeling scheme (PLS), functions as the distributed equivalent of NP, where a non-trustable prover assigns each node a certificate. Nodes exchange these certificates with their neighbors to prove the graph satisfies the predicate, with the certificate size being the primary complexity measure. Many graph properties, like planarity or bounded tree-width, can be certified with

O (\log n)

-bit certificates on n-node graphs.

This paper presents

O (\log n)

distributed certifications for recognizing geometric graph classes commonly found in distributed systems: interval graphs, chordal graphs, circular arc graphs, trapezoid graphs, and permutation graphs. It also establishes tight lower bounds on the certificate sizes required for these geometric intersection graph classes, proving that the proposed certifications are optimal.

分布式证明允许网络节点共同验证网络是否满足给定的谓词。最通用的机制，被称为证明标签方案（PLS），其功能相当于分布式NP，其中不可信任的证明者为每个节点分配证书。节点与其邻居交换这些证书，以证明图满足谓词，证书大小是主要的复杂性度量。许多图的性质，如平面性或有界树宽度，可以在n节点图上用O（log log n）位证书来证明。本文提出了O（log (n)）分布证明，用于识别分布系统中常见的几何图类：区间图、弦图、圆弧图、梯形图和置换图。它还建立了这些几何相交图类所需证书大小的严格下界，证明了所建议的证书是最优的。

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引用次数: 0

Finding diameter-reducing shortcuts in trees 在树上寻找减少直径的捷径

IF 1.1 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences

Pub Date : 2025-04-23 DOI: 10.1016/j.jcss.2025.103658

Davide Bilò , Luciano Gualà , Stefano Leucci , Luca Pepè Sciarria

In the k-Diameter-Optimally Augmenting Tree Problem we are given a tree T of n vertices embedded in an unknown metric space. An oracle can report the cost of any edge in constant time, and we want to augment T with k shortcuts to minimize the resulting diameter. When

k = 1

O (n \log n)

-time algorithms exist for paths and trees. We show that

o (n^{2})

queries cannot provide a better than 10/9-approximation for trees when

k \geq 3

. For any constant

ε > 0

, we design a linear-time

(1 + ε)

-approximation algorithm for paths when

k = o (\sqrt{\log n})

, thus establishing a dichotomy between paths and trees for

k \geq 3

. Our algorithm employs an ad-hoc data structure, which we also use in a linear-time 4-approximation algorithm for trees, and to compute the diameter of (possibly non-metric) graphs with

n + k - 1

edges in time

O (n k \log n)

在k-直径最优增广树问题中，我们给出了一棵树，其中有n个顶点嵌入在未知度量空间中。oracle可以在常数时间内报告任何边的成本，我们想用k个捷径来增加T，以最小化结果的直径。当k=1时，对于路径和树存在O（nlog (n)）时间算法。我们证明，当k≥3时，o（n2）查询不能提供优于10/9的近似。对于任意常数ε>；0，我们设计了k=o（log (n)）时路径的线性时间（1+ε）逼近算法，从而建立了k≥3时路径与树之间的二分类。我们的算法采用了一种特别的数据结构，我们也在树的线性时间4近似算法中使用它，并在时间O（nklog (n)）中计算具有n+k−1条边的（可能是非度量的）图的直径。

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