Theoretical Computer Science最新文献

英文中文

Privacy enhanced secure compact attribute-based signature from MQ problem for monotone span program 基于单调跨度程序 MQ 问题的隐私增强型安全紧凑属性签名

IF 0.9 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science

Pub Date : 2024-10-18 DOI: 10.1016/j.tcs.2024.114929

Jayashree Dey, Ratna Dutta

The rapid advancement of computer networks has led to an increase in the exposure of messages within an open environment (cloud). Therefore, the confidentiality of the user's signing information is extremely essential to handle unauthorized access and alterations. Attribute-based signature (ABS) scheme is a significant primitive that ensures the privacy of the user's signing information. To endorse a message, the signer can generate a signature with his/her attributes that satisfy a policy without revealing any other information. Post-quantum attribute-based signature schemes are attractive construction options whose safety do not collapse in presence of quantum computers. This article presents the first attribute-based signature scheme in multivariate quadratic (MQ) setting. To generate the secret signing key, the salted-UOV technique is employed in our protocol. While signing, the well-known 3-pass identification protocol is coupled with the Fiat-Shamir transformation. More positively, our candidate relies on presenting the policy as a monotone span program. We also study existential unforgeability and the perfect privacy feature which ensures that a signature cannot be linked to any signing information. Moreover, our scheme is compact in the sense that it performs efficiently in terms of storage when contrasted to the existing post-quantum attribute-based signature schemes.

计算机网络的快速发展导致信息在开放环境（云）中的曝光率增加。因此，用户签名信息的保密性对于处理未经授权的访问和篡改至关重要。基于属性的签名（ABS）方案是确保用户签名信息私密性的重要基础。要认可一条信息，签名者可以用他/她的属性生成一个符合策略的签名，而不会泄露任何其他信息。后量子属性签名方案是一种极具吸引力的构建方案，其安全性在量子计算机面前不会崩溃。本文提出了首个多变量二次方（MQ）环境下基于属性的签名方案。为了生成秘密签名密钥，我们的协议采用了加盐-UOV 技术。在签名时，著名的三重识别协议与 Fiat-Shamir 变换相结合。更积极的是，我们的候选方案依赖于将策略呈现为单调跨度程序。我们还研究了存在的不可伪造性和完美的隐私特性，确保签名不能与任何签名信息相关联。此外，与现有的基于后量子属性的签名方案相比，我们的方案结构紧凑，存储效率高。

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引用次数: 0

Diagrammatic calculus and generalized associativity for higher-arity tensor operations 图解微积分和高次张量运算的广义关联性

IF 0.9 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science

Pub Date : 2024-10-18 DOI: 10.1016/j.tcs.2024.114915

Carlos Zapata-Carratalá , Xerxes D. Arsiwalla , Taliesin Beynon

In this paper we investigate a ternary generalization of associativity by defining a diagrammatic calculus of hypergraphs that extends the usual notions of tensor networks, categories and relational algebras. Our key insight is to approach higher associativity as a confluence property of hypergraph rewrite systems. In doing so we rediscover the ternary structures known as heaps and are able to give a more comprehensive treatment of their emergence in the context of dagger categories and their generalizations. This approach allows us to define a notion of ternary category and heapoid, where morphisms bind three objects simultaneously, and suggests a systematic study of higher arity forms of associativity.

在本文中，我们研究了关联性的三元概括，定义了超图的图解微积分，扩展了张量网络、范畴和关系代数的通常概念。我们的主要见解是将高关联性作为超图重写系统的汇合属性来处理。这样，我们就重新发现了被称为堆的三元结构，并能在匕首范畴及其泛化的背景下更全面地处理它们的出现。通过这种方法，我们可以定义三元范畴和堆的概念，其中态同时绑定三个对象，并建议对关联性的更高层次形式进行系统研究。

引用次数: 0

A formalization of parallel data exchange algorithms used by numerical methods for solving partial differential equations 解决偏微分方程的数值方法所使用的并行数据交换算法的形式化

IF 0.9 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science

Pub Date : 2024-10-17 DOI: 10.1016/j.tcs.2024.114912

Cristóbal Samaniego, Guillaume Houzeaux

This paper introduces a formal framework for the data exchanges required to solve partial differential equations in a distributed memory parallel environment.

Many physical phenomena can be described in terms of partial differential equations, and discretization methods are commonly used to solve this class of equations. Most of them require the definition of a mesh or grid in order to discretize the problem domain. In a parallel programming environment, the original mesh is partitioned into subdomains. Then, important data that has a direct relationship with the original mesh will be also divided based on the partition. As a consequence, data between subdomains has to be exchanged in order to obtain the correct solution to the problem in parallel.

In this context, the main objective of this work is to describe the existing data exchange algorithms typically used in simulation codes by formal means. This objective is achieved by first describing the original and partitioned mesh in terms of set theory concepts and using them for writing the data exchange algorithms from the perspective of a typical implementation of three numerical methods: the finite element, finite difference, and cell-centered finite volume methods.

Some attempts to create a description for these algorithms can be found in the literature. However, in the authors' opinion, a formal description is necessary in order to avoid any ambiguity.

Implicit and explicit schemes are considered here. However, this study is primarily focused on implicit schemes where iterative methods are employed to solve the system of linear algebraic equations arising from the discretization of a partial differential equation in a parallel environment. These iterative methods serve as motivation for defining well-known data exchange algorithms necessary to solve the system of equations. To achieve this, we will first examine a simple one-dimensional problem, followed by a general problem description. We finally illustrate the concepts presented in the paper by examining the solution of a partial differential equation in parallel.

许多物理现象可以用偏微分方程来描述，离散化方法通常用于求解这类方程。大多数离散化方法都需要定义网格，以便将问题域离散化。在并行编程环境中，原始网格被划分为多个子域。然后，与原始网格有直接关系的重要数据也将根据分区进行划分。因此，必须在子域之间交换数据，才能并行获得问题的正确解决方案。在这种情况下，这项工作的主要目标是通过形式化手段描述仿真代码中通常使用的现有数据交换算法。为了实现这一目标，我们首先用集合论概念描述了原始网格和分割网格，并从有限元法、有限差分法和单元中心有限体积法这三种数值方法的典型实现角度，利用这些概念编写了数据交换算法。然而，作者认为，为了避免任何歧义，正式的描述是必要的。不过，本研究主要侧重于隐式方案，即在并行环境中采用迭代方法求解偏微分方程离散化产生的线性代数方程组。这些迭代法是定义解决方程系统所需的著名数据交换算法的动力。为此，我们将首先研究一个简单的一维问题，然后描述一般问题。最后，我们将通过研究偏微分方程的并行求解来说明本文提出的概念。

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引用次数: 0

Finding and counting small tournaments in large tournaments 在大型锦标赛中寻找和计算小型锦标赛

IF 0.9 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science

Pub Date : 2024-10-17 DOI: 10.1016/j.tcs.2024.114911

Raphael Yuster

We present new algorithms for counting and detecting small tournaments in a given tournament. In particular, we prove that every tournament on four vertices (there are four) can be detected in

O (n^{2})

time and counted in

O (n^{ω})

time where

ω < 2.372

is the matrix multiplication exponent. We further prove that any tournament on five vertices (there are 12) can be counted in

O (n^{ω + 1})

time. As for lower-bounds, we prove that for almost all k-vertex tournaments, the complexity of the detection problem is not easier than the complexity of the corresponding well-studied counting problem for undirected cliques of order

k - O (\log k)

我们提出了计算和检测给定锦标赛中的小型锦标赛的新算法。特别是，我们证明了四个顶点上的每场锦标赛（共有四场）都能在 O(n2) 时间内检测到，并在 O(nω) 时间内计数，其中 ω<2.372 是矩阵乘法指数。我们进一步证明，五个顶点上的任何锦标赛（共有 12 场）都能在 O(nω+1) 时间内计数。至于下限，我们证明了对于几乎所有 k 个顶点的锦标赛，检测问题的复杂度并不比针对阶数为 k-O(logk) 的无向小群的相应的、研究得很透彻的计数问题的复杂度更简单。

引用次数: 0

Truthful two-facility location with candidate locations 有候选地点的真实双设施地点

IF 0.9 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science

Pub Date : 2024-10-17 DOI: 10.1016/j.tcs.2024.114913

Panagiotis Kanellopoulos, Alexandros A. Voudouris, Rongsen Zhang

We study a truthful two-facility location problem in which a set of agents have private positions on the line of real numbers and known approval preferences over two different facilities. Given the locations of the two facilities, the cost of an agent is the total distance from the facilities she approves. The goal is to decide where to place the facilities from a given finite set of candidate locations so as to (a) approximately optimize desired social objectives, and (b) incentivize the agents to truthfully report their private positions. We focus on the class of deterministic strategyproof mechanisms and show bounds on their approximation ratio in terms of the social cost (i.e., the total cost of the agents) and the max cost for several classes of instances depending on the preferences of the agents over the facilities.

我们研究的是一个真实的双设施选址问题，在这个问题中，一组代理人在实数线上有私人位置，并且对两个不同设施的批准偏好是已知的。给定两个设施的位置后，代理人的成本就是与她所批准的设施之间的总距离。我们的目标是从给定的有限候选地点集合中决定在哪里放置设施，以便（a）近似优化所期望的社会目标，以及（b）激励代理人如实报告其私人立场。我们将重点放在确定性防策略机制类别上，并根据代理人对设施的偏好，展示了几类情况下社会成本（即代理人的总成本）和最大成本的近似率边界。

引用次数: 0

Path partitions of phylogenetic networks 系统发生网络的路径分区

IF 0.9 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science

Pub Date : 2024-10-16 DOI: 10.1016/j.tcs.2024.114907

Manuel Lafond , Vincent Moulton

In phylogenetics, evolution is traditionally represented in a tree-like manner. However, phylogenetic networks can be more appropriate for representing evolutionary events such as hybridization, horizontal gene transfer, and others. In particular, the class of forest-based networks was recently introduced to represent introgression, in which genes are swapped between species. A network is forest-based if it can be obtained by adding arcs to a collection of trees, so that the endpoints of the new arcs are in different trees. This contrasts with so-called tree-based networks, which are formed by adding arcs within a single tree.

We are interested in the computational complexity of recognizing forest-based networks, which was recently left as an open problem by Huber et al. It has been observed that forest-based networks coincide with directed acyclic graphs that can be partitioned into induced paths, each ending at a leaf of the original graph. Several types of path partitions have been studied in the graph theory literature, but to our best knowledge this type of ‘leaf induced path partition’ has not been directly considered before. The study of forest-based networks in terms of these partitions allows us to establish closer relationships between phylogenetics and algorithmic graph theory, and to provide answers to problems in both fields.

More specifically, we show that deciding whether a network is forest-based is NP-complete, even on input networks that are tree-based, binary, and have only three leaves. This shows that partitioning a directed acyclic graph into a constant number of induced paths is NP-complete, answering a recent question of Fernau et al. We then show that the problem is polynomial-time solvable on binary networks with two leaves and on the recently introduced class of orchards, which we show to be always forest-based. Finally, for undirected graphs, we introduce unrooted forest-based networks and provide hardness results for this class as well.

在系统发生学中，进化传统上以树状方式表示。然而，系统发育网络更适合表示杂交、水平基因转移等进化事件。特别是，最近引入了基于森林的网络来表示物种间基因交换的引入。如果可以通过在树集合中添加弧来获得网络，从而使新弧的端点位于不同的树中，那么该网络就是基于森林的网络。我们感兴趣的是识别森林网络的计算复杂性，这是 Huber 等人最近提出的一个悬而未决的问题。据观察，森林网络与有向无环图相吻合，这些有向无环图可以分割成诱导路径，每个诱导路径都以原始图的一片叶子为终点。图论文献中已经研究过几种类型的路径分区，但就我们所知，这种 "叶诱导路径分区 "还没有被直接考虑过。用这些分区来研究基于森林的网络，可以让我们在系统发生学和算法图论之间建立更密切的关系，并为这两个领域的问题提供答案。更具体地说，我们证明了决定一个网络是否基于森林是 NP-complete（不完全）的，即使输入网络是基于树的、二元的且只有三片叶子。这表明，将有向无环图分割成一定数量的诱导路径是 NP-complete，这回答了 Fernau 等人最近提出的一个问题。我们随后证明，在有两片叶子的二进制网络和最近引入的果园类上，该问题是多项式时间可解的，我们证明果园类总是基于森林的。最后，对于无向图，我们引入了无根森林网络，并给出了该类网络的硬度结果。

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引用次数: 0

Popularity on the roommate diversity problem 室友多样性问题的普及

IF 0.9 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science

Pub Date : 2024-10-15 DOI: 10.1016/j.tcs.2024.114903

Steven Ge, Toshiya Itoh

A recently introduced restricted variant of the multidimensional stable roommates problem is the roommate diversity problem: each agent belongs to one of two types (e.g., red and blue), and the agents' preferences over the rooms solely depend on the fraction of agents of their own type among their roommates. We study this variant with the notion of popularity.

We show that in the roommate diversity problem with the room size fixed to 2, the problem becomes tractable. Particularly, a popular partitioning of agents is guaranteed to exist and can be computed in polynomial time. Additionally, a mixed popular partitioning of agents is always guaranteed to exist in any roommate diversity game. By contrast, when there are no restrictions on the room size of a roommate diversity game, a popular partitioning may fail to exist and the problem becomes intractable.

室友多样性问题是多维稳定室友问题的一个新近引入的受限变体：每个代理都属于两种类型（如红色和蓝色）中的一种，代理对房间的偏好完全取决于室友中自己类型代理的比例。我们用 "受欢迎程度 "的概念研究了这一变量。我们发现，在室友多样性问题中，当房间大小固定为 2 时，问题变得很容易解决。我们的研究表明，在房间大小固定为 2 的室友多样性问题中，问题变得很容易解决。特别是，可以保证存在一个受欢迎的代理分区，并且可以在多项式时间内计算出来。此外，在任何室友多样性博弈中，都能保证存在一个混合的受欢迎的代理分区。相比之下，当室友多样性博弈的房间大小不受限制时，受欢迎的分区可能不存在，问题变得难以解决。

引用次数: 0

Sorting genomes by prefix double-cut-and-joins 通过前缀双切连接对基因组进行分类

IF 0.9 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science

Pub Date : 2024-10-15 DOI: 10.1016/j.tcs.2024.114909

Guillaume Fertin , Géraldine Jean , Anthony Labarre

In this paper, we study the problem of sorting unichromosomal linear genomes by prefix double-cut-and-joins (or DCJs) in both the signed and the unsigned settings. Prefix DCJs cut the leftmost segment of a genome and any other segment, and recombine the severed endpoints in one of two possible ways: one of these options corresponds to a prefix reversal, which reverses the order of elements between the two cuts (as well as their signs in the signed case). Our main results are: (1) new structural lower bounds based on the breakpoint graph for sorting by unsigned prefix reversals, unsigned prefix DCJs, and signed prefix DCJs; (2) two polynomial-time algorithms for sorting by prefix DCJs, both in the signed case (which answers an open question of Labarre [1]) and in the unsigned case; (3) a 1-absolute approximation algorithm for sorting by unsigned prefix reversals for a specific class of permutations.

在本文中，我们研究了在有符号和无符号两种情况下通过前缀双切连接（或 DCJ）对单染色体线性基因组进行排序的问题。前缀双切接法切割基因组最左边的片段和任何其他片段，并以两种可能的方式之一重组被切割的端点：其中一种方式对应于前缀反转，即颠倒两次切割之间元素的顺序（在有符号的情况下也颠倒元素的符号）。我们的主要成果有(1) 基于断点图的新结构下限，适用于无符号前缀反转、无符号前缀 DCJ 和有符号前缀 DCJ 排序；(2) 两种多项式时间算法，适用于有符号前缀 DCJ 排序（这回答了 Labarre [1] 提出的一个开放问题）和无符号前缀 DCJ 排序；(3) 一种 1-absolute 近似算法，适用于一类特定排列的无符号前缀反转排序。

引用次数: 0

On the existence of funneled orientations for classes of rooted phylogenetic networks 论有根系统发育网络的漏斗方向的存在性

IF 0.9 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science

Pub Date : 2024-10-15 DOI: 10.1016/j.tcs.2024.114908

Janosch Döcker, Simone Linz

Recently, there has been a growing interest in the relationships between unrooted and rooted phylogenetic networks. In this context, a natural question to ask is if an unrooted phylogenetic network

U

can be oriented as a rooted phylogenetic network such that the latter satisfies certain structural properties. In a recent preprint, Bulteau et al. claim that it is NP-hard to decide if

U

has a funneled (resp. funneled tree-child) orientation, for when the internal vertices of

U

have degree at most 5. Unfortunately, the proof of their funneled tree-child result appears to be incorrect. In this paper, we show that, despite their incorrect proof, it is NP-hard to decide if

U

has a funneled tree-child orientation even if each internal vertex has degree 5 and that NP-hardness remains for other popular classes of rooted phylogenetic networks such as funneled normal and funneled reticulation-visible. Additionally, our results hold regardless of whether

U

is rooted at an existing vertex or by subdividing an edge with the root.

最近，人们对无根系统发育网络和有根系统发育网络之间的关系越来越感兴趣。在这种情况下，一个自然而然的问题是，无根系统发育网络 U 是否可以定向为有根系统发育网络，从而使后者满足某些结构特性。在最近的预印本中，Bulteau 等人声称，当 U 的内部顶点阶数最多为 5 时，判断 U 是否具有漏斗状（或漏斗状树子）定向是 NP 难的。遗憾的是，他们对漏斗树子结果的证明似乎并不正确。在本文中，我们证明了尽管他们的证明不正确，但即使每个内部顶点的阶数都是 5，要判断 U 是否具有漏斗树子方向也是 NP-困难的，而且对于其他流行的有根系统发育网络类别，如漏斗正常和漏斗网状可见，NP-困难性依然存在。此外，无论 U 是根植于现有顶点还是通过细分根边，我们的结果都是成立的。

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引用次数: 0

Approximation algorithms for minimum ply covering of points with unit squares and unit disks 单位正方形和单位圆盘最小层覆盖点的近似计算算法

IF 0.9 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science

Pub Date : 2024-10-15 DOI: 10.1016/j.tcs.2024.114906

Stephane Durocher , J. Mark Keil , Debajyoti Mondal

Given a set P of points and a set U of geometric objects in the Euclidean plane, a minimum ply cover of P with U is a subset of U that covers P and minimizes the number of objects that share a common intersection, called the minimum ply cover number of P with U. Biedl et al. (2021) [9] showed that for both unit squares and unit disks, determining the minimum ply cover number for a set of points is NP-hard. They gave polynomial-time 2-approximation algorithms for the special case when the minimum ply cover number is constant, and asked whether there exists polynomial-time

O (1)

-approximation algorithms for these problems. In this paper, we settle the question posed by Biedl et al. by providing polynomial-time

O (1)

-approximation algorithms for the minimum ply cover problem for both unit squares and unit disks.

给定欧几里得平面中的一个点集 P 和一个几何对象集 U，P 与 U 的最小层覆盖是 U 的一个子集，该子集覆盖 P 并使共享一个共同交集的对象数目最小，称为 P 与 U 的最小层覆盖数。Biedl 等人（2021 年）[9] 的研究表明，对于单位正方形和单位圆盘，确定一个点集的最小层覆盖数都是 NP-困难的。他们给出了最小层覆盖数为常数时特殊情况下的多项式时间 2 近似算法，并询问是否存在针对这些问题的多项式时间 O(1)- 近似算法。在本文中，我们解决了 Biedl 等人提出的问题，为单位正方形和单位圆盘的最小层覆盖问题提供了多项式时间 O(1)- 近似算法。

引用次数: 0

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