Information Processing Letters最新文献

英文中文

An improved uniform convergence bound with fat-shattering dimension 具有碎脂维度的改进均匀收敛约束

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters

Pub Date : 2024-10-31 DOI: 10.1016/j.ipl.2024.106539

Roberto Colomboni , Emmanuel Esposito , Andrea Paudice

The fat-shattering dimension characterizes the uniform convergence property of real-valued function classes. The state-of-the-art upper bounds in [6] feature a multiplicative squared logarithmic factor on the sample complexity, leaving an open gap with the existing lower bound. By relying on a refined packing number bound given in [20], we provide an improved uniform convergence bound that closes this gap.

碎脂维度表征了实值函数类的均匀收敛特性。文献[6]中最先进的上界以样本复杂度的乘方对数因子为特征，与现有的下界存在差距。通过依赖 [20] 中给出的精炼堆积数边界，我们提供了一个改进的均匀收敛边界，缩小了这一差距。

引用次数: 0

Airports and railways with unsplittable demand 需求不可分割的机场和铁路

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters

Pub Date : 2024-10-28 DOI: 10.1016/j.ipl.2024.106538

Hossein Jowhari , Shamisa Nematollahi

In the problem of airports and railways with unsplittable demand (ARUD), we are given a complete graph

G = (V, E)

with weights on the vertices

a : V \to R^{+}

, and the length of the edges

ℓ : V \times V \to R^{+}

. Additionally, a positive integer k serves as the capacity parameter. We are also provided with a function

b : V \to N

that defines a non-zero demand for each city. The goal is to compute a spanning forest R of G and a subset

A \subseteq V

of minimum cost such that each component in R has one open facility and the total demand in each component is at most k (the capacity constraint). The cost of the solution

(A, R)

is defined as

\sum_{v \in A} a (v) + \sum_{e \in E (R)} ℓ (e)

. This problem is a generalization of the Airport and Railways (AR) problem introduced by Adamaszek et al. (STACS 2016). In Adamaszek et al. version, each vertex has a unit demand.

This paper presents a bi-criteria approximation algorithm for the metric ARUD problem in the sense that the algorithm is allowed to exceed the capacity constraints by

O (k)

while the cost of the solution is compared with the cost of an optimal solution that does not violate the capacity constraint. Our approach builds upon an existing approximation algorithm for the metric AR problem, developed by Adamaszek et al. (STACS 2018), and further leverages the well-known rounding algorithm of Shmoys and Tardos for the Generalized Assignment Problem (GAP). Assuming the total demand is polynomially bounded in the number of vertices, our algorithm runs in polynomial time. We also show that it is NP-hard to find an approximate solution for ARUD within any factor without violating the capacity constraints. This is the case even when each demand is polynomially bounded in the number of vertices. Furthermore, we determine the complexity of ARUD for some fixed values of k.

在需求不可分割的机场和铁路（ARUD）问题中，我们给定了一个完整的图 G=（V,E），其顶点的权重为 a:V→R+，边的长度为 ℓ:V×V→R+。此外，还有一个正整数 k 作为容量参数。我们还得到了一个函数 b:V→N，它定义了每个城市的非零需求。我们的目标是计算 G 的生成林 R 和成本最小的子集 A⊆V，使得 R 中的每个部分都有一个开放设施，且每个部分的总需求最多为 k（容量约束）。解 (A,R) 的成本定义为：∑v∈Aa(v)+∑e∈E(R)ℓ(e)。该问题是 Adamaszek 等人（STACS 2016）提出的机场与铁路（AR）问题的一般化。在 Adamaszek 等人的版本中，每个顶点都有一个单位需求。本文针对公制 ARUD 问题提出了一种双标准近似算法，即允许算法超出容量约束 O(k)，同时将解的成本与不违反容量约束的最优解的成本进行比较。我们的方法借鉴了 Adamaszek 等人（STACS 2018）针对度量 AR 问题开发的现有近似算法，并进一步利用了 Shmoys 和 Tardos 针对广义分配问题（GAP）的著名舍入算法。假设总需求在顶点数量上是多项式有界的，我们的算法将在多项式时间内运行。我们还证明，在不违反容量约束的情况下，在任何系数内找到 ARUD 的近似解都是 NP 难的。即使每个需求的顶点数都是多项式有界的，情况也是如此。此外，我们还确定了一些固定 k 值的 ARUD 复杂性。

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引用次数: 0

Reducing the space used by the sieve of Eratosthenes when factoring 减少埃拉托塞尼斯筛子在进行因式分解时使用的空间

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters

Pub Date : 2024-10-24 DOI: 10.1016/j.ipl.2024.106537

Samuel Hartman, Jonathan P. Sorenson

We present a version of the sieve of Eratosthenes that can factor all integers ≤x in

O (x \log \log x)

arithmetic operations using at most

O (\sqrt{x} / \log \log x)

bits of space. Among algorithms that take the optimal

O (x \log \log x)

time, this new space bound is an improvement of a factor proportional to

\log x \log \log x

over the implied previous bound of

O (\sqrt{x} \log x)

. We also show our algorithm performs well in practice.

我们提出了埃拉托塞尼斯筛的一个版本，它能在 O(xloglogx) 算术运算中对所有 ≤x 的整数进行因式分解，最多占用 O(x/loglogx) 比特空间。在最优时间为 O(xloglogx) 的算法中，这一新的空间约束比之前隐含的 O(xlogx) 约束提高了 logxloglogx 倍。我们还展示了我们的算法在实践中的良好表现。

引用次数: 0

An improved spectral lower bound of treewidth 改进的树宽光谱下界

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters

Pub Date : 2024-10-17 DOI: 10.1016/j.ipl.2024.106536

Tatsuya Gima , Tesshu Hanaka , Kohei Noro , Hirotaka Ono , Yota Otachi

We show that for every n-vertex graph with at least one edge, its treewidth is greater than or equal to

n λ_{2} / (Δ + λ_{2}) - 1

, where Δ and

λ_{2}

are the maximum degree and the second smallest Laplacian eigenvalue of the graph, respectively. This lower bound improves the one by Chandran and Subramanian [Inf. Process. Lett., 2003] and the subsequent one by the authors of the present paper [IEICE Trans. Inf. Syst., 2024]. The new lower bound is almost tight in the sense that there is an infinite family of graphs such that the lower bound is only 1 less than the treewidth for each graph in the family. Additionally, using similar techniques, we also present a lower bound of treewidth in terms of the largest and the second smallest Laplacian eigenvalues.

我们证明，对于每个至少有一条边的 n 顶点图，其树宽都大于或等于 nλ2/(Δ+λ2)-1，其中 Δ 和 λ2 分别是图的最大度和第二小拉普拉奇特征值。这个下界改进了 Chandran 和 Subramanian [Inf. Process. Lett.新的下界几乎是严密的，因为存在一个无限图族，使得下界只比族中每个图的树宽小 1。此外，利用类似的技术，我们还提出了最大和第二小拉普拉契亚特征值的树宽下界。

引用次数: 0

Tighter bound for generalized multiple discrete logarithm problem via MDS matrix method 通过 MDS 矩阵法实现广义多重离散对数问题的更严格约束

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters

Pub Date : 2024-10-16 DOI: 10.1016/j.ipl.2024.106535

Haoxuan Wu , Jincheng Zhuang

Discrete logarithm problem (DLP) is one of the fundamental hard problems used in cryptography. For

1 \leq k \leq n

, solving the k-out-of-n DLP instances is an important problem emerging in certain scenarios in public-key cryptography. Ying and Kunihiro (ACNS 2017) pioneered in studying k-out-of-n instance solutions of DLP, which is a generalized version of multiple DLP. By reducing the multiple DLP to the generalized version, they established lower bounds on the computational complexity of k-out-of-n DLP for different parameter values of k.

In this paper, we further reduce the reduction complexity presented in Ying and Kunihiro's work and increase the range of k and n for the tight lower bound of k-out-of-n DLP in the generic group model, which has applications in related cryptographic schemes. To achieve the goal, the key technique is to utilize a variant of fast multipoint evaluation. We divide the discussion into two cases. In the special case when n divides

p - 1

, by leveraging Number Theory Transform (NTT) technique, we expand k and n to a larger range. In the general case, by using a variant of fast multipoint evaluation, we increase k and n to a moderately larger range.

离散对数问题（DLP）是密码学中的基本难题之一。对于1≤k≤n，求解k-out-of-n DLP实例是公钥密码学某些场景中出现的重要问题。Ying和Kunihiro（ACSN 2017）率先研究了DLP的k-out-of-n实例解，这是多重DLP的广义版本。通过将多重 DLP 简化为广义版本，他们建立了不同参数值 k 的 k-out-of-n DLP 计算复杂度下限。本文进一步降低了 Ying 和 Kunihiro 工作中提出的简化复杂度，并增加了 k 和 n 的范围，从而在通用组模型中实现了 k-out-of-n DLP 的严格下限，这在相关密码方案中具有应用价值。为了实现这一目标，关键技术是利用快速多点评估的变体。我们将讨论分为两种情况。在 n 除以 p-1 的特殊情况下，利用数论变换（NTT）技术，我们可以将 k 和 n 扩展到更大的范围。在一般情况下，通过使用快速多点求值的变体，我们可以将 k 和 n 的范围适度扩大。

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引用次数: 0

Effective data reduction for strongly stable matching in very sparse graphs 非常稀疏图中强稳定匹配的有效数据缩减

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters

Pub Date : 2024-10-16 DOI: 10.1016/j.ipl.2024.106534

Rosa Wolf, Klaus Heeger , André Nichterlein

We provide a linear-time computable problem kernel of linear size for Strongly Stable Roommates parameterized by the feedback edge number of the acceptability graph (which encodes which agents may be matched to each other).

我们为 "强稳定室友"（Strongly Stable Roommates）提供了一个线性大小的线性时间可计算问题内核，该内核以可接受性图（可接受性图表示哪些代理可以相互匹配）的反馈边数为参数。

引用次数: 0

Counter abstraction for regular open teams 常规开放团队的反抽象

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters

Pub Date : 2024-09-16 DOI: 10.1016/j.ipl.2024.106533

Shabana A.T., Alphy George, S. Sheerazuddin

We study open swarms and teams of multi-agent systems where agents may join or leave the system at runtime. Kouvaros et al. [1] defined the verification problem for such systems and showed it to be undecidable, in general. Also, they have found one decidable class of open multi-agent systems and provided a partial decision procedure for another. In the same vein we present a subclass of open teams called regular open teams for which reachability is decidable. This is shown by employing a counter abstraction technique wherein the regular open team is abstracted into a finite state multi-counter system.

我们研究的是多代理系统的开放群和团队，其中的代理可以在运行时加入或离开系统。Kouvaros 等人[1]定义了这类系统的验证问题，并证明它在一般情况下是不可判定的。此外，他们还发现了一类可判定的开放式多代理系统，并为另一类系统提供了部分决策程序。同样，我们提出了一个开放团队的子类，称为常规开放团队，其可达性是可判定的。我们采用了一种计数器抽象技术，将常规开放团队抽象为有限状态多计数器系统，从而证明了这一点。

引用次数: 0

A 22k-approximation algorithm for minimum power k edge disjoint st-paths 最小功率 k 边相邻 st 路径的 22k 近似算法

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters

Pub Date : 2024-08-14 DOI: 10.1016/j.ipl.2024.106532

Zeev Nutov

In minimum power network design problems we are given an undirected graph $G = (V, E)$ with edge costs ${c_{e} : e \in E}$ . The goal is to find an edge set $F \subseteq E$ that satisfies a prescribed property of minimum power $p_{c} (F) = \sum_{v \in V} \max {c_{e} : e \in F is incident to v}$ . In the Min-Power k Edge Disjoint st-Paths problem F should contain k edge disjoint st-paths. The problem admits a k-approximation algorithm, and it was an open question to achieve an approximation ratio sublinear in k for simple graphs, even for unit costs. We give a $2 \sqrt{2 k}$ -approximation algorithm for general costs.

在最小功率网络设计问题中，我们给定了一个无向图 G=(V,E)，其边成本为 {ce:e∈E}。目标是找到满足最小功率 pc(F)=∑v∈Vmax{ce:e∈F is incident to v} 的规定属性的边集 F⊆E。在最小功率 k 边相邻 st 路径问题中，F 应包含 k 边相邻 st 路径。对于简单图，甚至对于单位成本，如何实现近似率亚线性于 k 是一个悬而未决的问题。我们给出了针对一般成本的 22k 近似算法。

引用次数: 0

Luby's MIS algorithms made self-stabilizing 卢比的管理信息系统算法实现了自稳定

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters

Pub Date : 2024-08-13 DOI: 10.1016/j.ipl.2024.106531

George Giakkoupis , Volker Turau , Isabella Ziccardi

We reconsider two well-known distributed randomized algorithms computing a maximal independent set, proposed in the seminal work of Luby (1986). We enhance these algorithms such that they become self-stabilizing without sacrificing their run-time, i.e., both stabilize in $O (\log n)$ synchronous rounds with high probability on any n-node graph. The first algorithm gets along with three states, but needs to know an upper bound on the maximum degree. The second does not need any information about the graph, but uses a number of states that is linear in the node degree. Both algorithms use messages of logarithmic size.

我们重新考虑了卢比（Luby，1986 年）的开创性工作中提出的计算最大独立集的两种著名分布式随机算法。我们对这些算法进行了改进，使它们在不牺牲运行时间的情况下实现自稳定，也就是说，在任何 n 个节点图上，这两种算法都能在 O(logn) 同步轮中高概率地实现稳定。第一种算法有三种状态，但需要知道最大度的上限。第二种算法不需要任何有关图的信息，但使用的状态数与节点度呈线性关系。两种算法都使用对数大小的信息。

引用次数: 0

Algorithms for subgraph complementation to some classes of graphs 某些类别图的子图补全算法

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters

Pub Date : 2024-08-13 DOI: 10.1016/j.ipl.2024.106530

Dhanyamol Antony , Sagartanu Pal , R.B. Sandeep

For a class $G$ of graphs, the objective of Subgraph Complementation to $G$ is to find whether there exists a subset S of vertices of the input graph G such that modifying G by complementing the subgraph induced by S results in a graph in $G$ . We obtain a polynomial-time algorithm for the problem when $G$ is the class of graphs with minimum degree at least k, for a constant k, answering an open problem by Fomin et al. (Algorithmica, 2020). When $G$ is the class of graphs without any induced copies of the star graph on $t + 1$ vertices (for any constant $t \geq 3$ ) and diamond, we obtain a polynomial-time algorithm for the problem. This is in contrast with a result by Antony et al. (Algorithmica, 2022) that the problem is NP-complete and cannot be solved in subexponential-time (assuming the Exponential Time Hypothesis) when $G$ is the class of graphs without any induced copies of the star graph on $t + 1$ vertices, for every constant $t \geq 5$ .

对于一类图 G，子图补全 G 的目标是找到输入图 G 的顶点是否存在一个子集 S，从而通过补全 S 诱导的子图来修改 G，从而得到 G 中的一个图。当 G 是最小度至少为 k 的一类图时，对于常数 k，我们得到了该问题的多项式时间算法，回答了 Fomin 等人提出的一个开放问题（Algorithmica, 2020）。当 G 是 t+1 个顶点上没有星形图的任何诱导副本（对于任意常数 t≥3）和菱形的图类时，我们得到了该问题的多项式时间算法。这与 Antony 等人（Algorithmica，2022 年）的结果形成鲜明对比：当 G 是一类没有任何星形图在 t+1 个顶点上的诱导副本的图时，对于每个常数 t≥5，该问题是 NP-完全的，并且无法在亚指数时间内求解（假设指数时间假设）。

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引用次数: 0

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