International Symposium on Algorithms and Computation最新文献

{"title":"Distance Queries over Dynamic Interval Graphs","authors":"Jingbang Chen, Meng He, J. I. Munro, Richard Peng, Kaiyu Wu, Daniel J. Zhang","doi":"10.4230/LIPIcs.ISAAC.2023.18","DOIUrl":"https://doi.org/10.4230/LIPIcs.ISAAC.2023.18","url":null,"abstract":"We design the first dynamic distance oracles for interval graphs, which are intersection graphs of a set of intervals on the real line, and for proper interval graphs, which are intersection graphs of a set of intervals in which no interval is properly contained in another. For proper interval graphs, we design a linear space data structure which supports distance queries (computing the distance between two query vertices) and vertex insertion or deletion in O (lg n ) worst-case time, where n is the number of vertices currently in G . Under incremental (insertion only) or decremental (deletion only) settings, we design linear space data structures that support distance queries in O (lg n ) worst-case time and vertex insertion or deletion in O (lg n ) amortized time, where n is the maximum number of vertices in the graph. Under fully dynamic settings, we design a data structure that represents an interval graph G in O ( n ) words of space to support distance queries in O ( n lg n/S ( n )) worst-case time and vertex insertion or deletion in O ( S ( n ) + lg n ) worst-case time, where n is the number of vertices currently in G and S ( n ) is an arbitrary function that satisfies S ( n ) = Ω(1) and S ( n ) = O ( n ). This implies an O ( n )-word solution with O ( √ n lg n )-time support for both distance queries and updates. All four data structures can answer shortest path queries by reporting the vertices in the shortest path between two query vertices in O (lg n ) worst-case time per vertex. We also study the hardness of supporting distance queries under updates over an intersection graph of 3D axis-aligned line segments, which generalizes our problem to 3D. Finally, we solve the problem of computing the diameter of a dynamic connected interval graph.","PeriodicalId":281888,"journal":{"name":"International Symposium on Algorithms and Computation","volume":"24 1","pages":"18:1-18:19"},"PeriodicalIF":0.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141041392","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":"FPT Approximation Using Treewidth: Capacitated Vertex Cover, Target Set Selection and Vector Dominating Set","authors":"Huairui Chu, Bingkai Lin","doi":"10.4230/LIPIcs.ISAAC.2023.19","DOIUrl":"https://doi.org/10.4230/LIPIcs.ISAAC.2023.19","url":null,"abstract":"Treewidth is a useful tool in designing graph algorithms. Although many NP-hard graph problems can be solved in linear time when the input graphs have small treewidth, there are problems which remain hard on graphs of bounded treewidth. In this paper, we consider three vertex selection problems that are W[1]-hard when parameterized by the treewidth of the input graph, namely the capacitated vertex cover problem, the target set selection problem and the vector dominating set problem. We provide two new methods to obtain FPT approximation algorithms for these problems. For the capacitated vertex cover problem and the vector dominating set problem, we obtain $(1+o(1))$-approximation FPT algorithms. For the target set selection problem, we give an FPT algorithm providing a tradeoff between its running time and the approximation ratio.","PeriodicalId":281888,"journal":{"name":"International Symposium on Algorithms and Computation","volume":" 12","pages":"19:1-19:20"},"PeriodicalIF":0.0,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138961408","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":"Streaming Algorithms for Graph k-Matching with Optimal or Near-Optimal Update Time","authors":"Jianer Chen, Qin Huang, Iyad A. Kanj, Qian Li, Ge Xia","doi":"10.4230/LIPIcs.ISAAC.2021.48","DOIUrl":"https://doi.org/10.4230/LIPIcs.ISAAC.2021.48","url":null,"abstract":"We present streaming algorithms for the graph $k$-matching problem in both the insert-only and dynamic models. Our algorithms, with space complexity matching the best upper bounds, have optimal or near-optimal update time, significantly improving on previous results. More specifically, for the insert-only streaming model, we present a one-pass algorithm with optimal space complexity $O(k^2)$ and optimal update time $O(1)$, that with high probability computes a maximum weighted $k$-matching of a given weighted graph. The update time of our algorithm significantly improves the previous upper bound of $O(log k)$, which was derived only for $k$-matching on unweighted graphs. For the dynamic streaming model, we present a one-pass algorithm that with high probability computes a maximum weighted $k$-matching in $O(Wk^2 cdot mbox{polylog}(n)$ space and with $O(mbox{polylog}(n))$ update time, where $W$ is the number of distinct edge weights. Again the update time of our algorithm improves the previous upper bound of $O(k^2 cdot mbox{polylog}(n))$. This algorithm, when applied to unweighted graphs, gives a streaming algorithm on the dynamic model whose space and update time complexities are both near-optimal. Our results also imply a streaming approximation algorithm for maximum weighted $k$-matching whose space complexity matches the best known upper bound with a significantly improved update time.","PeriodicalId":281888,"journal":{"name":"International Symposium on Algorithms and Computation","volume":"193 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133690164","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":"Clustering with Faulty Centers","authors":"K. Fox, Hongyao Huang, Benjamin Raichel","doi":"10.4230/LIPIcs.ISAAC.2022.10","DOIUrl":"https://doi.org/10.4230/LIPIcs.ISAAC.2022.10","url":null,"abstract":"In this paper we introduce and formally study the problem of k -clustering with faulty centers. Specifically, we study the faulty versions of k -center, k -median, and k -means clustering, where centers have some probability of not existing, as opposed to prior work where clients had some probability of not existing. For all three problems we provide fixed parameter tractable algorithms, in the parameters k , d , and ε , that (1 + ε )-approximate the minimum expected cost solutions for points in d dimensional Euclidean space. For Faulty k -center we additionally provide a 5-approximation for general metrics. Significantly, all of our algorithms have a small dependence on n . Specifically, our Faulty k -center algorithms have only linear dependence on n , while for our algorithms for Faulty k -median and Faulty k -means the dependence is still only n 1+ o (1) . 2012 ACM Subject Classification","PeriodicalId":281888,"journal":{"name":"International Symposium on Algorithms and Computation","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134422469","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":"Unbounded Regions of High-Order Voronoi Diagrams of Lines and Segments in Higher Dimensions","authors":"G. Barequet, Evanthia Papadopoulou, Martin Suderland","doi":"10.4230/LIPIcs.ISAAC.2019.62","DOIUrl":"https://doi.org/10.4230/LIPIcs.ISAAC.2019.62","url":null,"abstract":"<jats:p>We study the behavior at infinity of the farthest and the higher-order Voronoi diagram of <jats:italic>n</jats:italic> line segments or lines in a <jats:italic>d</jats:italic>-dimensional Euclidean space. The unbounded parts of these diagrams can be encoded by a <jats:italic>Gaussian map</jats:italic> on the sphere of directions <jats:inline-formula><jats:alternatives><jats:tex-math>$$mathbb {S}^{d-1}$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\u0000 <mml:msup>\u0000 <mml:mrow>\u0000 <mml:mi>S</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mrow>\u0000 <mml:mi>d</mml:mi>\u0000 <mml:mo>-</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:mrow>\u0000 </mml:msup>\u0000 </mml:math></jats:alternatives></jats:inline-formula>. We show that the combinatorial complexity of the Gaussian map for the order-<jats:italic>k</jats:italic> Voronoi diagram of <jats:italic>n</jats:italic> line segments and lines is <jats:inline-formula><jats:alternatives><jats:tex-math>$$O(min {k,n-k}n^{d-1})$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\u0000 <mml:mrow>\u0000 <mml:mi>O</mml:mi>\u0000 <mml:mo>(</mml:mo>\u0000 <mml:mo>min</mml:mo>\u0000 <mml:mrow>\u0000 <mml:mo>{</mml:mo>\u0000 <mml:mi>k</mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mo>-</mml:mo>\u0000 <mml:mi>k</mml:mi>\u0000 <mml:mo>}</mml:mo>\u0000 </mml:mrow>\u0000 <mml:msup>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mrow>\u0000 <mml:mi>d</mml:mi>\u0000 <mml:mo>-</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:mrow>\u0000 </mml:msup>\u0000 <mml:mo>)</mml:mo>\u0000 </mml:mrow>\u0000 </mml:math></jats:alternatives></jats:inline-formula>, which is tight for <jats:inline-formula><jats:alternatives><jats:tex-math>$$n-k=O(1)$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\u0000 <mml:mrow>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mo>-</mml:mo>\u0000 <mml:mi>k</mml:mi>\u0000 <mml:mo>=</mml:mo>\u0000 <mml:mi>O</mml:mi>\u0000 <mml:mo>(</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo>)</mml:mo>\u0000 </mml:mrow>\u0000 </mml:math></jats:alternatives></jats:inline-formula>. This exactly reflects the combinatorial complexity of the unbounded features of these diagrams. All the <jats:italic>d</jats:italic>-dimensional cells of the farthest Voronoi diagram are unbounded, its <jats:inline-formula><jats:alternatives><jats:tex-math>$$(d-1)$$</jats:tex-math><mml:math xmlns:mml=\"http://","PeriodicalId":281888,"journal":{"name":"International Symposium on Algorithms and Computation","volume":"160 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114583898","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":"Subquadratic Weighted Matroid Intersection Under Rank Oracles","authors":"Ta-Wei Tu","doi":"10.48550/arXiv.2212.00508","DOIUrl":"https://doi.org/10.48550/arXiv.2212.00508","url":null,"abstract":"Given two matroids $mathcal{M}_1 = (V, mathcal{I}_1)$ and $mathcal{M}_2 = (V, mathcal{I}_2)$ over an $n$-element integer-weighted ground set $V$, the weighted matroid intersection problem aims to find a common independent set $S^{*} in mathcal{I}_1 cap mathcal{I}_2$ maximizing the weight of $S^{*}$. In this paper, we present a simple deterministic algorithm for weighted matroid intersection using $tilde{O}(nr^{3/4}log{W})$ rank queries, where $r$ is the size of the largest intersection of $mathcal{M}_1$ and $mathcal{M}_2$ and $W$ is the maximum weight. This improves upon the best previously known $tilde{O}(nrlog{W})$ algorithm given by Lee, Sidford, and Wong [FOCS'15], and is the first subquadratic algorithm for polynomially-bounded weights under the standard independence or rank oracle models. The main contribution of this paper is an efficient algorithm that computes shortest-path trees in weighted exchange graphs.","PeriodicalId":281888,"journal":{"name":"International Symposium on Algorithms and Computation","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114328138","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":"Unique-Neighbor-Like Expansion and Group-Independent Cosystolic Expansion","authors":"T. Kaufman, David Mass","doi":"10.4230/LIPIcs.ISAAC.2021.56","DOIUrl":"https://doi.org/10.4230/LIPIcs.ISAAC.2021.56","url":null,"abstract":"In recent years, high dimensional expanders have been found to have a variety of applications in theoretical computer science, such as efficient CSPs approximations, improved sampling and list-decoding algorithms, and more. Within that, an important high dimensional expansion notion is emph{cosystolic expansion}, which has found applications in the construction of efficiently decodable quantum codes and in proving lower bounds for CSPs. Cosystolic expansion is considered with systems of equations over a group where the variables and equations correspond to faces of the complex. Previous works that studied cosystolic expansion were tailored to the specific group $mathbb{F}_2$. In particular, Kaufman, Kazhdan and Lubotzky (FOCS 2014), and Evra and Kaufman (STOC 2016) in their breakthrough works, who solved a famous open question of Gromov, have studied a notion which we term ``parity'' expansion for small sets. They showed that small sets of $k$-faces have proportionally many $(k+1)$-faces that contain emph{an odd number} of $k$-faces from the set. Parity expansion for small sets could be used to imply cosystolic expansion only over $mathbb{F}_2$. In this work we introduce a stronger emph{unique-neighbor-like} expansion for small sets. We show that small sets of $k$-faces have proportionally many $(k+1)$-faces that contain emph{exactly one} $k$-face from the set. This notion is fundamentally stronger than parity expansion and cannot be implied by previous works. We then show, utilizing the new unique-neighbor-like expansion notion introduced in this work, that cosystolic expansion can be made emph{group-independent}, i.e., unique-neighbor-like expansion for small sets implies cosystolic expansion emph{over any group}.","PeriodicalId":281888,"journal":{"name":"International Symposium on Algorithms and Computation","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130476171","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":"External-memory dictionaries with worst-case update cost","authors":"Rathish Das, J. Iacono, Yakov Nekrich","doi":"10.48550/arXiv.2211.06044","DOIUrl":"https://doi.org/10.48550/arXiv.2211.06044","url":null,"abstract":"The $B^{epsilon}$-tree [Brodal and Fagerberg 2003] is a simple I/O-efficient external-memory-model data structure that supports updates orders of magnitude faster than B-tree with a query performance comparable to the B-tree: for any positive constant $epsilon<1$ insertions and deletions take $O(frac{1}{B^{1-epsilon}}log_{B}N)$ time (rather than $O(log_BN)$ time for the classic B-tree), queries take $O(log_BN)$ time and range queries returning $k$ items take $O(log_BN+frac{k}{B})$ time. Although the $B^{epsilon}$-tree has an optimal update/query tradeoff, the runtimes are amortized. Another structure, the write-optimized skip list, introduced by Bender et al. [PODS 2017], has the same performance as the $B^{epsilon}$-tree but with runtimes that are randomized rather than amortized. In this paper, we present a variant of the $B^{epsilon}$-tree with deterministic worst-case running times that are identical to the original's amortized running times.","PeriodicalId":281888,"journal":{"name":"International Symposium on Algorithms and Computation","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114461016","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":"Hierarchical Categories in Colored Searching","authors":"P. Afshani, Rasmus Killmann, Kasper Green Larsen","doi":"10.48550/arXiv.2210.05403","DOIUrl":"https://doi.org/10.48550/arXiv.2210.05403","url":null,"abstract":"In colored range counting (CRC), the input is a set of points where each point is assigned a ``color'' (or a ``category'') and the goal is to store them in a data structure such that the number of distinct categories inside a given query range can be counted efficiently. CRC has strong motivations as it allows data structure to deal with categorical data. However, colors (i.e., the categories) in the CRC problem do not have any internal structure, whereas this is not the case for many datasets in practice where hierarchical categories exists or where a single input belongs to multiple categories. Motivated by these, we consider variants of the problem where such structures can be represented. We define two variants of the problem called hierarchical range counting (HCC) and sub-category colored range counting (SCRC) and consider hierarchical structures that can either be a DAG or a tree. We show that the two problems on some special trees are in fact equivalent to other well-known problems in the literature. Based on these, we also give efficient data structures when the underlying hierarchy can be represented as a tree. We show a conditional lower bound for the general case when the existing hierarchy can be any DAG, through reductions from the orthogonal vectors problem.","PeriodicalId":281888,"journal":{"name":"International Symposium on Algorithms and Computation","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134322775","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":"Multi-Robot Motion Planning for Unit Discs with Revolving Areas","authors":"P. Agarwal, Tzvika Geft, D. Halperin, Erin Taylor","doi":"10.4230/LIPIcs.ISAAC.2022.35 10.1016/j.comgeo.2023.102019","DOIUrl":"https://doi.org/10.4230/LIPIcs.ISAAC.2022.35 10.1016/j.comgeo.2023.102019","url":null,"abstract":"We study the problem of motion planning for a collection of $n$ labeled unit disc robots in a polygonal environment. We assume that the robots have revolving areas around their start and final positions: that each start and each final is contained in a radius $2$ disc lying in the free space, not necessarily concentric with the start or final position, which is free from other start or final positions. This assumption allows a weakly-monotone motion plan, in which robots move according to an ordering as follows: during the turn of a robot $R$ in the ordering, it moves fully from its start to final position, while other robots do not leave their revolving areas. As $R$ passes through a revolving area, a robot $R'$ that is inside this area may move within the revolving area to avoid a collision. Notwithstanding the existence of a motion plan, we show that minimizing the total traveled distance in this setting, specifically even when the motion plan is restricted to be weakly-monotone, is APX-hard, ruling out any polynomial-time $(1+epsilon)$-approximation algorithm. On the positive side, we present the first constant-factor approximation algorithm for computing a feasible weakly-monotone motion plan. The total distance traveled by the robots is within an $O(1)$ factor of that of the optimal motion plan, which need not be weakly monotone. Our algorithm extends to an online setting in which the polygonal environment is fixed but the initial and final positions of robots are specified in an online manner. Finally, we observe that the overhead in the overall cost that we add while editing the paths to avoid robot-robot collision can vary significantly depending on the ordering we chose. Finding the best ordering in this respect is known to be NP-hard, and we provide a polynomial time $O(log n log log n)$-approximation algorithm for this problem.","PeriodicalId":281888,"journal":{"name":"International Symposium on Algorithms and Computation","volume":"174 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116115920","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}