arXiv - CS - Data Structures and Algorithms最新文献_第6页

Scalable Neighborhood Local Search for Single-Machine Scheduling with Family Setup Times 具有家庭设置时间的单机调度的可扩展邻域本地搜索

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-09-01 DOI: arxiv-2409.00771

Kaja Balzereit, Niels Grüttemeier, Nils Morawietz, Dennis Reinhardt, Stefan Windmann, Petra Wolf

{"title":"Scalable Neighborhood Local Search for Single-Machine Scheduling with Family Setup Times","authors":"Kaja Balzereit, Niels Grüttemeier, Nils Morawietz, Dennis Reinhardt, Stefan Windmann, Petra Wolf","doi":"arxiv-2409.00771","DOIUrl":"https://doi.org/arxiv-2409.00771","url":null,"abstract":"In this work, we study the task of scheduling jobs on a single machine with\u0000sequence dependent family setup times under the goal of minimizing the\u0000makespan, that is, the completion time of the last job in the schedule. This\u0000notoriously NP-hard problem is highly relevant in practical productions and\u0000requires heuristics that provide good solutions quickly in order to deal with\u0000large instances. In this paper, we present a heuristic based on the approach of\u0000parameterized local search. That is, we aim to replace a given solution by a\u0000better solution having distance at most $k$ in a pre-defined distance measure.\u0000This is done multiple times in a hill-climbing manner, until a locally optimal\u0000solution is reached. We analyze the trade-off between the allowed distance $k$\u0000and the algorithm's running time for four natural distance measures. Example of\u0000allowed operations for our considered distance measures are: swapping $k$ pairs\u0000of jobs in the sequence, or rearranging $k$ consecutive jobs. For two distance\u0000measures, we show that finding an improvement for given $k$ can be done in\u0000$f(k) cdot n^{mathcal{O}(1)}$ time, while such a running time for the other\u0000two distance measures is unlikely. We provide a preliminary experimental\u0000evaluation of our local search approaches.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Persistent Hierarchical Bloom Filter-based Framework for Authentication and Tracking of ICs 基于分层布卢姆过滤器的集成电路认证和跟踪持久框架

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-08-30 DOI: arxiv-2408.16950

Md Mashfiq Rizvee, Tanvir Hossain, Tamzidul Hoque, Domenic Forte, Sumaiya Shomaji

引用次数: 0

Preprocessing to Reduce the Search Space for Odd Cycle Transversal 减少奇数周期横向搜索空间的预处理方法

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-08-30 DOI: arxiv-2409.00245

Bart M. P. Jansen, Yosuke Mizutani, Blair D. Sullivan, Ruben F. A. Verhaegh

{"title":"Preprocessing to Reduce the Search Space for Odd Cycle Transversal","authors":"Bart M. P. Jansen, Yosuke Mizutani, Blair D. Sullivan, Ruben F. A. Verhaegh","doi":"arxiv-2409.00245","DOIUrl":"https://doi.org/arxiv-2409.00245","url":null,"abstract":"The NP-hard Odd Cycle Transversal problem asks for a minimum vertex set whose\u0000removal from an undirected input graph $G$ breaks all odd cycles, and thereby\u0000yields a bipartite graph. The problem is well-known to be fixed-parameter\u0000tractable when parameterized by the size $k$ of the desired solution. It also\u0000admits a randomized kernelization of polynomial size, using the celebrated\u0000matroid toolkit by Kratsch and Wahlstr\"{o}m. The kernelization guarantees a\u0000reduction in the total $textit{size}$ of an input graph, but does not\u0000guarantee any decrease in the size of the solution to be sought; the latter\u0000governs the size of the search space for FPT algorithms parameterized by $k$.\u0000We investigate under which conditions an efficient algorithm can detect one or\u0000more vertices that belong to an optimal solution to Odd Cycle Transversal. By\u0000drawing inspiration from the popular $textit{crown reduction}$ rule for Vertex\u0000Cover, and the notion of $textit{antler decompositions}$ that was recently\u0000proposed for Feedback Vertex Set, we introduce a graph decomposition called\u0000$textit{tight odd cycle cut}$ that can be used to certify that a vertex set is\u0000part of an optimal odd cycle transversal. While it is NP-hard to compute such a\u0000graph decomposition, we develop parameterized algorithms to find a set of at\u0000least $k$ vertices that belong to an optimal odd cycle transversal when the\u0000input contains a tight odd cycle cut certifying the membership of $k$ vertices\u0000in an optimal solution. The resulting algorithm formalizes when the search\u0000space for the solution-size parameterization of Odd Cycle Transversal can be\u0000reduced by preprocessing. To obtain our results, we develop a graph reduction\u0000step that can be used to simplify the graph to the point that the odd cycle cut\u0000can be detected via color coding.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Unfairly Splitting Separable Necklaces 不公平地拆分可分离的项链

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-08-30 DOI: arxiv-2408.17126

Patrick Schnider, Linus Stalder, Simon Weber

{"title":"Unfairly Splitting Separable Necklaces","authors":"Patrick Schnider, Linus Stalder, Simon Weber","doi":"arxiv-2408.17126","DOIUrl":"https://doi.org/arxiv-2408.17126","url":null,"abstract":"The Necklace Splitting problem is a classical problem in combinatorics that\u0000has been intensively studied both from a combinatorial and a computational\u0000point of view. It is well-known that the Necklace Splitting problem reduces to\u0000the discrete Ham Sandwich problem. This reduction was crucial in the proof of\u0000PPA-completeness of the Ham Sandwich problem. Recently, Borzechowski, Schnider\u0000and Weber [ISAAC'23] introduced a variant of Necklace Splitting that similarly\u0000reduces to the $alpha$-Ham Sandwich problem, which lies in the complexity\u0000class UEOPL but is not known to be complete. To make this reduction work, the\u0000input necklace is guaranteed to be n-separable. They showed that these\u0000necklaces can be fairly split in polynomial time and thus this subproblem\u0000cannot be used to prove UEOPL-hardness for $alpha$-Ham Sandwich. We consider\u0000the more general unfair necklace splitting problem on n-separable necklaces,\u0000i.e., the problem of splitting these necklaces such that each thief gets a\u0000desired fraction of each type of jewels. This more general problem is the\u0000natural necklace-splitting-type version of $alpha$-Ham Sandwich, and its\u0000complexity status is one of the main open questions posed by Borzechowski,\u0000Schnider and Weber. We show that the unfair splitting problem is also\u0000polynomial-time solvable, and can thus also not be used to show UEOPL-hardness\u0000for $alpha$-Ham Sandwich.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

E-Graphs as Circuits, and Optimal Extraction via Treewidth 作为电路的电子图，以及通过树宽进行优化提取

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-08-30 DOI: arxiv-2408.17042

Glenn Sun, Yihong Zhang, Haobin Ni

引用次数: 0

Online Probabilistic Metric Embedding: A General Framework for Bypassing Inherent Bounds 在线概率度量嵌入：绕过固有限制的通用框架

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-08-29 DOI: arxiv-2408.16298

Yair Bartal, Ora N. Fandina, Seeun William Umboh

{"title":"Online Probabilistic Metric Embedding: A General Framework for Bypassing Inherent Bounds","authors":"Yair Bartal, Ora N. Fandina, Seeun William Umboh","doi":"arxiv-2408.16298","DOIUrl":"https://doi.org/arxiv-2408.16298","url":null,"abstract":"Probabilistic metric embedding into trees is a powerful technique for\u0000designing online algorithms. The standard approach is to embed the entire\u0000underlying metric into a tree metric and then solve the problem on the latter.\u0000The overhead in the competitive ratio depends on the expected distortion of the\u0000embedding, which is logarithmic in $n$, the size of the underlying metric. For\u0000many online applications, such as online network design problems, it is natural\u0000to ask if it is possible to construct such embeddings in an online fashion such\u0000that the distortion would be a polylogarithmic function of $k$, the number of\u0000terminals. Our first main contribution is answering this question negatively, exhibiting\u0000a emph{lower bound} of $tilde{Omega}(log k log Phi)$, where $Phi$ is the\u0000aspect ratio of the set of terminals, showing that a simple modification of the\u0000probabilistic embedding into trees of Bartal (FOCS 1996), which has expected\u0000distortion of $O(log k log Phi)$, is emph{nearly-tight}. Unfortunately,\u0000this may result in a very bad dependence in terms of $k$, namely, a power of\u0000$k$. Our second main contribution is a general framework for bypassing this\u0000limitation. We show that for a large class of online problems this online\u0000probabilistic embedding can still be used to devise an algorithm with\u0000$O(min{log klog (klambda),log^3 k})$ overhead in the competitive ratio,\u0000where $k$ is the current number of terminals, and $lambda$ is a measure of\u0000subadditivity of the cost function, which is at most $r$, the current number of\u0000requests. In particular, this implies the first algorithms with competitive\u0000ratio $operatorname{polylog}(k)$ for online subadditive network design\u0000(buy-at-bulk network design being a special case), and\u0000$operatorname{polylog}(k,r)$ for online group Steiner forest.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202674","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Improving Lagarias-Odlyzko Algorithm For Average-Case Subset Sum: Modular Arithmetic Approach 改进平均情况下子集和的 Lagarias-Odlyzko 算法：模块化算术方法

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-08-28 DOI: arxiv-2408.16108

Antoine Joux, Karol Węgrzycki

{"title":"Improving Lagarias-Odlyzko Algorithm For Average-Case Subset Sum: Modular Arithmetic Approach","authors":"Antoine Joux, Karol Węgrzycki","doi":"arxiv-2408.16108","DOIUrl":"https://doi.org/arxiv-2408.16108","url":null,"abstract":"Lagarias and Odlyzko (J.~ACM~1985) proposed a polynomial time algorithm for\u0000solving ``emph{almost all}'' instances of the Subset Sum problem with $n$\u0000integers of size $Omega(Gamma_{text{LO}})$, where\u0000$log_2(Gamma_{text{LO}}) > n^2 log_2(gamma)$ and $gamma$ is a parameter\u0000of the lattice basis reduction ($gamma > sqrt{4/3}$ for LLL). The algorithm\u0000of Lagarias and Odlyzko is a cornerstone result in cryptography. However, the\u0000theoretical guarantee on the density of feasible instances has remained\u0000unimproved for almost 40 years. In this paper, we propose an algorithm to solve ``almost all'' instances of\u0000Subset Sum with integers of size $Omega(sqrt{Gamma_{text{LO}}})$ after a\u0000single call to the lattice reduction. Additionally, our argument allows us to\u0000solve the Subset Sum problem for multiple targets while the previous approach\u0000could only answer one target per call to lattice basis reduction. We introduce\u0000a modular arithmetic approach to the Subset Sum problem. The idea is to use the\u0000lattice reduction to solve a linear system modulo a suitably large prime. We\u0000show that density guarantees can be improved, by analysing the lengths of the\u0000LLL reduced basis vectors, of both the primal and the dual lattices\u0000simultaneously.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

When to Give Up on a Parallel Implementation 何时放弃并行实施

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-08-28 DOI: arxiv-2408.16092

Nathan S. Sheffield, Alek Westover

{"title":"When to Give Up on a Parallel Implementation","authors":"Nathan S. Sheffield, Alek Westover","doi":"arxiv-2408.16092","DOIUrl":"https://doi.org/arxiv-2408.16092","url":null,"abstract":"In the Serial Parallel Decision Problem (SPDP), introduced by Kuszmaul and\u0000Westover [SPAA'24], an algorithm receives a series of tasks online, and must\u0000choose for each between a serial implementation and a parallelizable (but less\u0000efficient) implementation. Kuszmaul and Westover describe three decision\u0000models: (1) defn{Instantly-committing} schedulers must decide on arrival,\u0000irrevocably, which implementation of the task to run. (2)\u0000defn{Eventually-committing} schedulers can delay their decision beyond a\u0000task's arrival time, but cannot revoke their decision once made. (3)\u0000defn{Never-committing} schedulers are always free to abandon their progress on\u0000the task and start over using a different implementation. Kuszmaul and Westover\u0000gave a simple instantly-committing scheduler whose total completion time is\u0000$3$-competitive with the offline optimal schedule. They conjectured that the\u0000three decision models should admit different competitive ratios, but left upper\u0000bounds below $3$ in any model as an open problem. In this paper, we show that the powers of instantly, eventually, and never\u0000committing schedulers are distinct, at least in the ``massively parallel\u0000regime''. The massively parallel regime of the SPDP is the special case where\u0000the number of available processors is asymptotically larger than the number of\u0000tasks to process, meaning that the emph{work} associated with running a task\u0000in serial is negligible compared to its emph{runtime}. In this regime, we show\u0000(1) The optimal competitive ratio for instantly-committing schedulers is $2$,\u0000(2) The optimal competitive ratio for eventually-committing schedulers lies in\u0000$[1.618, 1.678]$, (3) The optimal competitive ratio for never-committing\u0000schedulers lies in $[1.366, 1.500]$.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Weighted Matching in the Random-Order Streaming and Robust Communication Models 随机顺序流和稳健通信模型中的加权匹配

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-08-27 DOI: arxiv-2408.15434

Diba Hashemi, Weronika Wrzos-Kaminska

{"title":"Weighted Matching in the Random-Order Streaming and Robust Communication Models","authors":"Diba Hashemi, Weronika Wrzos-Kaminska","doi":"arxiv-2408.15434","DOIUrl":"https://doi.org/arxiv-2408.15434","url":null,"abstract":"We study the maximum weight matching problem in the random-order\u0000semi-streaming model and in the robust communication model. Unlike many other\u0000sublinear models, in these two frameworks, there is a large gap between the\u0000guarantees of the best known algorithms for the unweighted and weighted\u0000versions of the problem. In the random-order semi-streaming setting, the edges of an $n$-vertex graph\u0000arrive in a stream in a random order. The goal is to compute an approximate\u0000maximum weight matching with a single pass over the stream using $O(ntext{\u0000polylog } n)$ space. Our main result is a $(2/3-epsilon)$-approximation\u0000algorithm for maximum weight matching in random-order streams, using space $O(n\u0000log n log R)$, where $R$ is the ratio between the heaviest and the lightest\u0000edge in the graph. Our result nearly matches the best known unweighted\u0000$(2/3+epsilon_0)$-approximation (where $epsilon_0 sim 10^{-14}$ is a small\u0000constant) achieved by Assadi and Behnezhad [ICALP 2021], and significantly\u0000improves upon previous weighted results. Our techniques also extend to the related robust communication model, in\u0000which the edges of a graph are partitioned randomly between Alice and Bob.\u0000Alice sends a single message of size $O(ntext{ polylog }n)$ to Bob, who must\u0000compute an approximate maximum weight matching. We achieve a\u0000$(5/6-epsilon)$-approximation using $O(n log n log R)$ words of\u0000communication, matching the results of Azarmehr and Behnezhad [ICALP 2023] for\u0000unweighted graphs.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On Controlling Knockout Tournaments Without Perfect Information 在信息不完全的情况下控制淘汰赛

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-08-27 DOI: arxiv-2408.15068

Václav Blažej, M. S. Ramanujan, Peter Strulo, Sushmita Gupta

引用次数: 0