Theoretical Computer Science最新文献

{"title":"Approximation results on resource leveling problems","authors":"Pascale Bendotti ,&nbsp;Luca Brunod-Indrigo ,&nbsp;Philippe Chrétienne ,&nbsp;Bruno Escoffier","doi":"10.1016/j.tcs.2025.115430","DOIUrl":"10.1016/j.tcs.2025.115430","url":null,"abstract":"<div><div>This work deals with resource leveling problems. A set of jobs is given as well as a resource level representing a capacity that may be exceeded at some cost. Jobs have integer processing times, must be scheduled non-preemptively and consume one unit of resource while processed. More precisely, the objective to be maximized is the resource use below the resource level, i.e., the complementary of the total overload cost.</div><div>Two main families of problems are investigated: either with or without precedence constraints. The case with no precedence constraints is shown to admit an EPTAS; a quasi-linear time approximation algorithm with constant ratio <span><math><mfrac><mrow><mn>7</mn></mrow><mrow><mn>8</mn></mrow></mfrac></math></span> is also provided. The case with precedence constraints is shown to be significantly harder to solve as it does not admit a PTAS under some classical complexity assumption. Approximation algorithms with constant ratios are provided for special cases with in-tree precedence graph or with fixed resource level.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1053 ","pages":"Article 115430"},"PeriodicalIF":0.9,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144580184","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fast simulations of the multi-album collector","authors":"D. Barak-Pelleg ,&nbsp;D. Berend","doi":"10.1016/j.tcs.2025.115432","DOIUrl":"10.1016/j.tcs.2025.115432","url":null,"abstract":"<div><div>Our starting point is the coupon collector's problem (CCP). In this problem, there are <em>n</em> coupons that are drawn uniformly randomly with replacement. The question is how many drawings on average are needed to collect at least one copy (or some other predetermined number <em>m</em> of copies) of each coupon?</div><div>The problem may be traced back to the 18-th century, having been mentioned already by de Moivre. Numerous questions have been posed based on the problem since its inception, and it turned out to appear naturally in many applications.</div><div>A naive simulation of the process is trivial to implement. However, the runtime of this algorithm makes it impractical for large values of <em>n</em>. We present here an alternative view of the coupon collecting process, for coupons with any probabilities, that allows us to increase the range of <em>n</em>-s (and <em>m</em>-s) for which the simulation may be run. For equi-probable coupons, we present additional improvements, making the simulation possible in a very short time practically for any <em>n</em>. More precisely, we show that the runtime of our algorithm is <span><math><mi>Θ</mi><mo>(</mo><mi>m</mi><mo>+</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span>.</div><div>We present theoretical results concerning some of the quantities relevant to our algorithms and conduct simulations to test the algorithms in practice.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1053 ","pages":"Article 115432"},"PeriodicalIF":0.9,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144571082","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Matching cut and variants on bipartite graphs of bounded radius and diameter","authors":"Felicia Lucke","doi":"10.1016/j.tcs.2025.115429","DOIUrl":"10.1016/j.tcs.2025.115429","url":null,"abstract":"<div><div>In the <span>Matching Cut</span> problem we ask whether a graph <em>G</em> has a matching cut, that is, a matching which is also an edge cut of <em>G</em>. We consider the variants <span>Perfect Matching Cut</span> and <span>Disconnected Perfect Matching</span> where we ask whether there exists a matching cut equal to, respectively, contained in a perfect matching. In addition, in the problem <span>Maximum Matching Cut</span> we ask for a matching cut with a maximum number of edges. The last problem we consider is <em>d</em><span>-Cut</span> where we ask for an edge cut where each vertex is incident to at most <em>d</em> edges in the cut.</div><div>We investigate the computational complexity of these problems on bipartite graphs of bounded radius and diameter. Our results extend known results for <span>Matching Cut</span> and <span>Disconnected Perfect Matching</span>. We give complexity dichotomies for <em>d</em><span>-Cut</span> and <span>Maximum Matching Cut</span> and solve one of two open cases for <span>Disconnected Perfect Matching</span>. For <span>Perfect Matching Cut</span> we give the first hardness result for bipartite graphs of bounded radius and diameter and extend the known polynomial cases.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1052 ","pages":"Article 115429"},"PeriodicalIF":0.9,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144517915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Retraction notice to “Corrigendum to ‘A New Approximation Algorithm for the Minimum 2-Edge-Connected Spanning Subgraph Problem”\" [Theoretical computer science 963 (2023) 113926]","authors":"A. Çivril","doi":"10.1016/j.tcs.2025.115427","DOIUrl":"10.1016/j.tcs.2025.115427","url":null,"abstract":"","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1052 ","pages":"Article 115427"},"PeriodicalIF":0.9,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144481559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A quantum speedup algorithm for TSP based on quantum dynamic programming with very few qubits","authors":"Xujun Bai ,&nbsp;Yun Shang","doi":"10.1016/j.tcs.2025.115423","DOIUrl":"10.1016/j.tcs.2025.115423","url":null,"abstract":"<div><div>The Traveling Salesman Problem (TSP) is a classical NP-hard problem that plays a crucial role in combinatorial optimization. In this paper, we are interested in the quantum search framework for the TSP because it has robust theoretical guarantees. However, we need to first search for all Hamiltonian cycles from a very large solution space, which greatly weakens the advantage of quantum search algorithms. To address this issue, one can first prepare a superposition state of all feasible solutions, and then amplify the amplitude of the optimal solution from it. We propose a quantum algorithm to generate the uniform superposition state of all N-length Hamiltonian cycles as an initial state within polynomial gate complexity based on pure quantum dynamic programming with very few ancillary qubits, which achieves exponential acceleration compared to the previous initial state preparation algorithm. As a result, we realized the theoretical minimum query complexity of quantum search algorithms for a general TSP. Compared to some algorithms that theoretically have lower query complexities but lack practical implementation solutions, our algorithm has feasible circuit implementation.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1052 ","pages":"Article 115423"},"PeriodicalIF":0.9,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144490693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Clustering under a knapsack constraint: Parameterized approximation for the knapsack median problem","authors":"Zhen Zhang ,&nbsp;Zhuohang Gao ,&nbsp;Limei Liu ,&nbsp;Yao Liu ,&nbsp;Jie Chen ,&nbsp;Qilong Feng","doi":"10.1016/j.tcs.2025.115426","DOIUrl":"10.1016/j.tcs.2025.115426","url":null,"abstract":"<div><div>The <span>Knapsack Median</span> problem, defined over a set of clients and facilities in a metric space, seeks to open a subset of facilities and connect each client to an opened facility, with the goal of minimizing the sum of client-connection costs while keeping the sum of facility-opening costs within a specified budget. Solving this problem exactly in FPT time, parameterized by the maximum number of opened facilities (denoted by <em>k</em>), is unlikely due to its W[2]-hardness. Thus, we focus on parameterized approximation algorithms for the problem. We give a sampling-based method that reduces the solution search space, which yields a <span><math><mo>(</mo><mn>3</mn><mo>+</mo><mi>ε</mi><mo>)</mo></math></span>-approximation algorithm running in <span><math><msup><mrow><mo>(</mo><mi>k</mi><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow><mrow><mi>O</mi><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><msup><mrow><mi>n</mi></mrow><mrow><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msup></math></span> time in general metric spaces and a <span><math><mo>(</mo><mn>1</mn><mo>+</mo><mi>ε</mi><mo>)</mo></math></span>-approximation algorithm with similar running time in <em>d</em>-dimensional Euclidean space.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1052 ","pages":"Article 115426"},"PeriodicalIF":0.9,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144490690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Subnetwork reliability analysis about complete-transposition graph networks","authors":"Qun Chen,&nbsp;Qingying Deng,&nbsp;Kainan Xiang","doi":"10.1016/j.tcs.2025.115421","DOIUrl":"10.1016/j.tcs.2025.115421","url":null,"abstract":"<div><div>As multiprocessor computer systems expand in size and complexity, the probability of encountering faulty processors within the system also increases. Understanding and evaluating the impact of these faulty processors on the entire system is critical. Reliability assessment serves as a key metric for quantifying the effect of faulty processors on the overall system performance. A widely used method for evaluating system reliability is to compute the probability that a fault-free subsystem of a given size remains operational when the system contains some faulty processors. A higher probability indicates greater system reliability. In this paper, we utilize the probability fault model and the Inclusion-Exclusion principle to analyze the <span><math><mi>C</mi><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></math></span> subnetwork reliability of <span><math><mi>C</mi><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> under node failures. We derive the upper and lower bounds on the <span><math><mi>C</mi><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></math></span>-reliability of the <span><math><mi>C</mi><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> by analyzing the intersection of up to five <span><math><mi>C</mi><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></math></span> subnetworks. Furthermore, our findings demonstrate that the theoretical results closely match simulation results, particularly when the single-node reliability value <em>p</em> is low.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1053 ","pages":"Article 115421"},"PeriodicalIF":0.9,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144534608","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quantum algorithms for one-sided crossing minimization","authors":"Susanna Caroppo,&nbsp;Giordano Da Lozzo,&nbsp;Giuseppe Di Battista","doi":"10.1016/j.tcs.2025.115424","DOIUrl":"10.1016/j.tcs.2025.115424","url":null,"abstract":"<div><div>We present singly-exponential quantum algorithms for the <span>One-Sided Crossing Minimization</span> (OSCM) problem. Given an <em>n</em>-vertex bipartite graph <span><math><mi>G</mi><mo>=</mo><mo>(</mo><mi>U</mi><mo>,</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>⊆</mo><mi>U</mi><mo>×</mo><mi>V</mi><mo>)</mo></math></span>, a 2<em>-level drawing</em> <span><math><mo>(</mo><msub><mrow><mi>π</mi></mrow><mrow><mi>U</mi></mrow></msub><mo>,</mo><msub><mrow><mi>π</mi></mrow><mrow><mi>V</mi></mrow></msub><mo>)</mo></math></span> of <em>G</em> is described by a linear ordering <span><math><msub><mrow><mi>π</mi></mrow><mrow><mi>U</mi></mrow></msub><mo>:</mo><mi>U</mi><mo>↔</mo><mo>{</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mo>|</mo><mi>U</mi><mo>|</mo><mo>}</mo></math></span> of <em>U</em> and linear ordering <span><math><msub><mrow><mi>π</mi></mrow><mrow><mi>V</mi></mrow></msub><mo>:</mo><mi>V</mi><mo>↔</mo><mo>{</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mo>|</mo><mi>V</mi><mo>|</mo><mo>}</mo></math></span> of <em>V</em>. For a fixed linear ordering <span><math><msub><mrow><mi>π</mi></mrow><mrow><mi>U</mi></mrow></msub></math></span> of <em>U</em>, the OSCM problem seeks to find a linear ordering <span><math><msub><mrow><mi>π</mi></mrow><mrow><mi>V</mi></mrow></msub></math></span> of <em>V</em> that yields a 2-level drawing <span><math><mo>(</mo><msub><mrow><mi>π</mi></mrow><mrow><mi>U</mi></mrow></msub><mo>,</mo><msub><mrow><mi>π</mi></mrow><mrow><mi>V</mi></mrow></msub><mo>)</mo></math></span> of <em>G</em> with the minimum number of edge crossings. We show that OSCM can be viewed as a set problem over <em>V</em> amenable for exact algorithms with a quantum speedup with respect to their classical counterparts. First, we exploit the quantum dynamic programming framework of Ambainis et al. [<em>Quantum Speedups for Exponential-Time Dynamic Programming Algorithms</em>. SODA 2019] to devise a QRAM-based algorithm that solves OSCM in <span><math><msup><mrow><mi>O</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><msup><mrow><mn>1.728</mn></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span> time and space. Second, we use quantum divide and conquer to obtain an algorithm that solves OSCM without using QRAM in <span><math><msup><mrow><mi>O</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span> time and polynomial space.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1052 ","pages":"Article 115424"},"PeriodicalIF":0.9,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144364782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Approximation algorithms for facility location and k-median with differential privacy","authors":"Lu Wang ,&nbsp;Qilong Feng ,&nbsp;Jianxin Wang","doi":"10.1016/j.tcs.2025.115417","DOIUrl":"10.1016/j.tcs.2025.115417","url":null,"abstract":"<div><div>In this paper we consider the problems of facility location and <em>k</em>-median with differential privacy in metric space, where a local search-based framework is proposed to solve the differential privacy issues. The approximation algorithm given for the facility location problem has a multiplicative error of 4 and an additive error of <span><math><mi>O</mi><mo>(</mo><mi>Δ</mi><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>log</mi><mo>⁡</mo><mi>n</mi><mi>log</mi><mo>⁡</mo><mo>(</mo><mi>n</mi><mo>+</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>max</mi></mrow></msub><msup><mrow><mi>Δ</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo></math></span>, where <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>max</mi></mrow></msub></math></span> is the maximum facility-opening cost, <em>n</em> is the number of clients, and Δ is the maximum distance between any two input points. For the <em>k</em>-median problem, our local search-based framework yields an approximation algorithm with a multiplicative error of <span><math><mn>4</mn><mo>+</mo><mi>ε</mi></math></span> and an additive error of <span><math><mi>O</mi><mo>(</mo><mi>Δ</mi><msup><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mi>log</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>⁡</mo><mi>n</mi><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo>)</mo></math></span>.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1052 ","pages":"Article 115417"},"PeriodicalIF":0.9,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144481558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the complexity of list H-packing for sparse graph classes","authors":"Tatsuya Gima ,&nbsp;Tesshu Hanaka ,&nbsp;Yasuaki Kobayashi ,&nbsp;Yota Otachi ,&nbsp;Tomohito Shirai ,&nbsp;Akira Suzuki ,&nbsp;Yuma Tamura ,&nbsp;Xiao Zhou","doi":"10.1016/j.tcs.2025.115425","DOIUrl":"10.1016/j.tcs.2025.115425","url":null,"abstract":"<div><div>The problem of packing as many subgraphs isomorphic to some <span><math><mi>H</mi><mo>∈</mo><mi>H</mi></math></span> as possible into a graph, where <span><math><mi>H</mi></math></span> is a collection of graphs, has been well studied in the literature. Both vertex-disjoint and edge-disjoint versions are known to be NP-complete for <em>H</em> that contains at least three vertices and at least three edges, respectively. In this paper, we consider “list variants” of these problems: Given a graph <em>G</em>, an integer <em>k</em>, and a collection <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>H</mi></mrow></msub></math></span> of subgraphs of <em>G</em> isomorphic to some <span><math><mi>H</mi><mo>∈</mo><mi>H</mi></math></span>, the goal is to compute <em>k</em> subgraphs in <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>H</mi></mrow></msub></math></span> that are pairwise vertex- or edge-disjoint. We show several positive and negative results, focusing on classes of sparse graphs, such as bounded-degree graphs, planar graphs, and bounded-treewidth graphs.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1052 ","pages":"Article 115425"},"PeriodicalIF":0.9,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144490691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}