E. Bampis, B. Escoffier, Niklas Hahn, Michalis Xefteris
{"title":"Online TSP with Known Locations","authors":"E. Bampis, B. Escoffier, Niklas Hahn, Michalis Xefteris","doi":"10.48550/arXiv.2210.14722","DOIUrl":"https://doi.org/10.48550/arXiv.2210.14722","url":null,"abstract":"In this paper, we consider the Online Traveling Salesperson Problem (OLTSP) where the locations of the requests are known in advance, but not their arrival times. We study both the open variant, in which the algorithm is not required to return to the origin when all the requests are served, as well as the closed variant, in which the algorithm has to return to the origin after serving all the requests. Our aim is to measure the impact of the extra knowledge of the locations on the competitiveness of the problem. We present an online 3/2-competitive algorithm for the general case and a matching lower bound for both the open and the closed variant. Then, we focus on some interesting metric spaces (ring, star, semi-line), providing both lower bounds and polynomial time online algorithms for the problem.","PeriodicalId":380945,"journal":{"name":"Workshop on Algorithms and Data Structures","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124515983","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}
Julia Baligacs, Y. Disser, Farehe Soheil, David Weckbecker
{"title":"Tight Analysis of the Lazy Algorithm for Open Online Dial-a-Ride","authors":"Julia Baligacs, Y. Disser, Farehe Soheil, David Weckbecker","doi":"10.1007/978-3-031-38906-1_4","DOIUrl":"https://doi.org/10.1007/978-3-031-38906-1_4","url":null,"abstract":"","PeriodicalId":380945,"journal":{"name":"Workshop on Algorithms and Data Structures","volume":"184 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127049090","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}
{"title":"Realizability Makes a Difference: A Complexity Gap for Sink-Finding in USOs","authors":"Simon Weber, Joel Widmer","doi":"10.48550/arXiv.2207.05985","DOIUrl":"https://doi.org/10.48550/arXiv.2207.05985","url":null,"abstract":"Algorithms for finding the sink in Unique Sink Orientations (USOs) of the hypercube can be used to solve many algebraic and geometric problems, most importantly including the P-Matrix Linear Complementarity Problem and Linear Programming. The realizable USOs are those that arise from the reductions of these problems to the USO sink-finding problem. Finding the sink of realizable USOs is thus highly practically relevant, yet it is unknown whether realizability can be exploited algorithmically to find the sink more quickly. However, all (non-trivial) known unconditional lower bounds for sink-finding make use of USOs that are provably not realizable. This indicates that the sink-finding problem might indeed be strictly easier on realizable USOs. In this paper we show that this is true for a subclass of all USOs. We consider the class of Matouv{s}ek-type USOs, which are a translation of Matouv{s}ek's LP-type problems into the language of USOs. We show a query complexity gap between sink-finding in all, and sink-finding in only the realizable $n$-dimensional Matouv{s}ek-type USOs. We provide concrete deterministic algorithms and lower bounds for both cases, and show that in the realizable case $O(log^2 n)$ vertex evaluation queries suffice, while in general exactly $n$ queries are needed. The Matouv{s}ek-type USOs are the first USO class found to admit such a gap.","PeriodicalId":380945,"journal":{"name":"Workshop on Algorithms and Data Structures","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131171668","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}
Rusul Alsaedi, Joachim Gudmundsson, André van Renssen
{"title":"The Mutual Visibility Problem for Fat Robots","authors":"Rusul Alsaedi, Joachim Gudmundsson, André van Renssen","doi":"10.48550/arXiv.2206.14423","DOIUrl":"https://doi.org/10.48550/arXiv.2206.14423","url":null,"abstract":"Given a set of $n geq 1$ unit disk robots in the Euclidean plane, we consider the fundamental problem of providing mutual visibility to them: the robots must reposition themselves to reach a configuration where they all see each other. This problem arises under obstructed visibility, where a robot cannot see another robot if there is a third robot on the straight line segment between them. This problem was solved by Sharma et al. [G. Sharma, R. Alsaedi, C. Busch, and S. Mukhopadhyay. The complete visibility problem for fat robots with lights. In Proceedings of the 19th International Conference on Distributed Computing and Networking, pages 1-4, 2018.] in the luminous robots model, where each robot is equipped with an externally visible light that can assume colors from a fixed set of colors, using 9 colors and $O(n)$ rounds. In this work, we present an algorithm that requires only 2 colors and $O(n)$ rounds. The number of colors is optimal since at least two colors are required for point robots [G.A. Di Luna, P. Flocchini, S.G. Chaudhuri, F. Poloni, N. Santoro, and G. Viglietta. Mutual visibility by luminous robots without collisions. Information and Computation, 254:392-418, 2017.].","PeriodicalId":380945,"journal":{"name":"Workshop on Algorithms and Data Structures","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115134909","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}
Jingbang Chen, Yu Gao, Yufan Huang, Richard Peng, Runze Wang
{"title":"Hardness of Graph-Structured Algebraic and Symbolic Problems","authors":"Jingbang Chen, Yu Gao, Yufan Huang, Richard Peng, Runze Wang","doi":"10.1007/978-3-031-38906-1_16","DOIUrl":"https://doi.org/10.1007/978-3-031-38906-1_16","url":null,"abstract":"","PeriodicalId":380945,"journal":{"name":"Workshop on Algorithms and Data Structures","volume":"378 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124713842","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}
{"title":"General Space-Time Tradeoffs via Relational Queries","authors":"Shaleen Deep, Xiao Hu, Paraschos Koutris","doi":"10.1007/978-3-031-38906-1_21","DOIUrl":"https://doi.org/10.1007/978-3-031-38906-1_21","url":null,"abstract":"","PeriodicalId":380945,"journal":{"name":"Workshop on Algorithms and Data Structures","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128345517","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}
{"title":"Support Optimality and Adaptive Cuckoo Filters","authors":"T. Kopelowitz, Samuel McCauley, E. Porat","doi":"10.1007/978-3-030-83508-8_40","DOIUrl":"https://doi.org/10.1007/978-3-030-83508-8_40","url":null,"abstract":"","PeriodicalId":380945,"journal":{"name":"Workshop on Algorithms and Data Structures","volume":"430 24","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113998544","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}
{"title":"Uniform Embeddings for Robinson Similarity Matrices","authors":"J. Janssen, Zhiyuan Zhang","doi":"10.1007/978-3-030-83508-8_36","DOIUrl":"https://doi.org/10.1007/978-3-030-83508-8_36","url":null,"abstract":"","PeriodicalId":380945,"journal":{"name":"Workshop on Algorithms and Data Structures","volume":"545 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133304945","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}
{"title":"Scheduling with Testing on Multiple Identical Parallel Machines","authors":"S. Albers, Alexander Eckl","doi":"10.1007/978-3-030-83508-8_3","DOIUrl":"https://doi.org/10.1007/978-3-030-83508-8_3","url":null,"abstract":"","PeriodicalId":380945,"journal":{"name":"Workshop on Algorithms and Data Structures","volume":" 19","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132074890","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}
{"title":"Reverse Shortest Path Problem for Unit-Disk Graphs","authors":"Haitao Wang, Yiming Zhao","doi":"10.1007/978-3-030-83508-8_47","DOIUrl":"https://doi.org/10.1007/978-3-030-83508-8_47","url":null,"abstract":"","PeriodicalId":380945,"journal":{"name":"Workshop on Algorithms and Data Structures","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115494798","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}