Scandinavian Workshop on Algorithm Theory最新文献_第2页

Most Classic Problems Remain NP-hard on Relative Neighborhood Graphs and their Relatives 大多数经典问题仍然是相对邻域图及其近亲上的np困难问题

Scandinavian Workshop on Algorithm Theory Pub Date : 2021-07-09 DOI: 10.4230/LIPIcs.SWAT.2022.29

Pascal Kunz, T. Fluschnik, R. Niedermeier, Malte Renken

引用次数: 0

Compacting Squares 压实广场

Scandinavian Workshop on Algorithm Theory Pub Date : 2021-05-17 DOI: 10.4230/LIPIcs.SWAT.2022.4

I. Kostitsyna, I. Parada, Willem Sonke, B. Speckmann, J. Wulms

{"title":"Compacting Squares","authors":"I. Kostitsyna, I. Parada, Willem Sonke, B. Speckmann, J. Wulms","doi":"10.4230/LIPIcs.SWAT.2022.4","DOIUrl":"https://doi.org/10.4230/LIPIcs.SWAT.2022.4","url":null,"abstract":"A well-established theoretical model for modular robots in two dimensions are edge-connected configurations of square modules, which can reconfigure through so-called sliding moves. Dumitrescu and Pach [Graphs and Combinatorics, 2006] proved that it is always possible to reconfigure one edge-connected configuration of $n$ squares into any other using at most $O(n^2)$ sliding moves, while keeping the configuration connected at all times. For certain pairs of configurations, reconfiguration may require $Omega(n^2)$ sliding moves. However, significantly fewer moves may be sufficient. We prove that it is NP-hard to minimize the number of sliding moves for a given pair of edge-connected configurations. On the positive side we present Gather&Compact, an input-sensitive in-place algorithm that requires only $O(bar{P} n)$ sliding moves to transform one configuration into the other, where $bar{P}$ is the maximum perimeter of the two bounding boxes. The squares move within the bounding boxes only, with the exception of at most one square at a time which may move through the positions adjacent to the bounding boxes. The $O(bar{P} n)$ bound never exceeds $O(n^2)$, and is optimal (up to constant factors) among all bounds parameterized by just $n$ and $bar{P}$. Our algorithm is built on the basic principle that well-connected components of modular robots can be transformed efficiently. Hence we iteratively increase the connectivity within a configuration, to finally arrive at a single solid $xy$-monotone component. We implemented Gather&Compact and compared it experimentally to the in-place modification by Moreno and Sacrist'an [EuroCG 2020] of the Dumitrescu and Pach algorithm (MSDP). Our experiments show that Gather&Compact consistently outperforms MSDP by a significant margin, on all types of square configurations.","PeriodicalId":447445,"journal":{"name":"Scandinavian Workshop on Algorithm Theory","volume":"80 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122025804","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: 4

On the Approximability of the Traveling Salesman Problem with Line Neighborhoods 带线邻域的旅行商问题的逼近性

Scandinavian Workshop on Algorithm Theory Pub Date : 2020-08-27 DOI: 10.4230/LIPIcs.SWAT.2022.10

A. Antoniadis, Sándor Kisfaludi-Bak, Bundit Laekhanukit, Daniel Vaz

{"title":"On the Approximability of the Traveling Salesman Problem with Line Neighborhoods","authors":"A. Antoniadis, Sándor Kisfaludi-Bak, Bundit Laekhanukit, Daniel Vaz","doi":"10.4230/LIPIcs.SWAT.2022.10","DOIUrl":"https://doi.org/10.4230/LIPIcs.SWAT.2022.10","url":null,"abstract":"We study the variant of the Euclidean Traveling Salesman problem where instead of a set of points, we are given a set of lines as input, and the goal is to find the shortest tour that visits each line. The best known upper and lower bounds for the problem in $mathbb{R}^d$, with $dge 3$, are $mathrm{NP}$-hardness and an $O(log^3 n)$-approximation algorithm which is based on a reduction to the group Steiner tree problem. \u0000We show that TSP with lines in $mathbb{R}^d$ is APX-hard for any $dge 3$. More generally, this implies that TSP with $k$-dimensional flats does not admit a PTAS for any $1le k leq d-2$ unless $mathrm{P}=mathrm{NP}$, which gives a complete classification of the approximability of these problems, as there are known PTASes for $k=0$ (i.e., points) and $k=d-1$ (hyperplanes). We are able to give a stronger inapproximability factor for $d=O(log n)$ by showing that TSP with lines does not admit a $(2-epsilon)$-approximation in $d$ dimensions under the unique games conjecture. On the positive side, we leverage recent results on restricted variants of the group Steiner tree problem in order to give an $O(log^2 n)$-approximation algorithm for the problem, albeit with a running time of $n^{O(loglog n)}$.","PeriodicalId":447445,"journal":{"name":"Scandinavian Workshop on Algorithm Theory","volume":"49 407 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123371223","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

Algorithms for the Discrete Fréchet Distance Under Translation 翻译条件下离散帧距离的算法

Scandinavian Workshop on Algorithm Theory Pub Date : 2020-06-18 DOI: 10.4230/LIPIcs.SWAT.2018.20

O. Filtser, M. J. Katz

{"title":"Algorithms for the Discrete Fréchet Distance Under Translation","authors":"O. Filtser, M. J. Katz","doi":"10.4230/LIPIcs.SWAT.2018.20","DOIUrl":"https://doi.org/10.4230/LIPIcs.SWAT.2018.20","url":null,"abstract":"The (discrete) Frechet distance (DFD) is a popular similarity measure for curves. Often the input curves are not aligned, so one of them must undergo some transformation for the distance computation to be meaningful. Ben Avraham et al. [Rinat Ben Avraham et al., 2015] presented an O(m^3n^2(1+log(n/m))log(m+n))-time algorithm for DFD between two sequences of points of sizes m and n in the plane under translation. In this paper we consider two variants of DFD, both under translation.\u0000For DFD with shortcuts in the plane, we present an O(m^2n^2 log^2(m+n))-time algorithm, by presenting a dynamic data structure for reachability queries in the underlying directed graph. In 1D, we show how to avoid the use of parametric search and remove a logarithmic factor from the running time of (the 1D versions of) these algorithms and of an algorithm for the weak discrete Frechet distance; the resulting running times are thus O(m^2n(1+log(n/m))), for the discrete Frechet distance, and O(mn log(m+n)), for its two variants.\u0000Our 1D algorithms follow a general scheme introduced by Martello et al. [Martello et al., 1984] for the Balanced Optimization Problem (BOP), which is especially useful when an efficient dynamic version of the feasibility decider is available. We present an alternative scheme for BOP, whose advantage is that it yields efficient algorithms quite easily, without having to devise a specially tailored dynamic version of the feasibility decider. We demonstrate our scheme on the most uniform path problem (significantly improving the known bound), and observe that the weak DFD under translation in 1D is a special case of it.","PeriodicalId":447445,"journal":{"name":"Scandinavian Workshop on Algorithm Theory","volume":"125 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129599364","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: 6

Locality Sensitive Hashing for Set-Queries, Motivated by Group Recommendations 基于组推荐的集合查询的局部性敏感哈希

Scandinavian Workshop on Algorithm Theory Pub Date : 2020-04-15 DOI: 10.4230/LIPIcs.SWAT.2020.28

Haim Kaplan, J. Tenenbaum

{"title":"Locality Sensitive Hashing for Set-Queries, Motivated by Group Recommendations","authors":"Haim Kaplan, J. Tenenbaum","doi":"10.4230/LIPIcs.SWAT.2020.28","DOIUrl":"https://doi.org/10.4230/LIPIcs.SWAT.2020.28","url":null,"abstract":"Locality Sensitive Hashing (LSH) is an effective method to index a set of points such that we can efficiently find the nearest neighbors of a query point. We extend this method to our novel Set-query LSH (SLSH), such that it can find the nearest neighbors of a set of points, given as a query. \u0000Let $ s(x,y) $ be the similarity between two points $ x $ and $ y $. We define a similarity between a set $ Q$ and a point $ x $ by aggregating the similarities $ s(p,x) $ for all $ pin Q $. For example, we can take $ s(p,x) $ to be the angular similarity between $ p $ and $ x $ (i.e., $1-{angle (x,p)}/{pi}$), and aggregate by arithmetic or geometric averaging, or taking the lowest similarity. \u0000We develop locality sensitive hash families and data structures for a large set of such arithmetic and geometric averaging similarities, and analyze their collision probabilities. We also establish an analogous framework and hash families for distance functions. Specifically, we give a structure for the euclidean distance aggregated by either averaging or taking the maximum. \u0000We leverage SLSH to solve a geometric extension of the approximate near neighbors problem. In this version, we consider a metric for which the unit ball is an ellipsoid and its orientation is specified with the query. \u0000An important application that motivates our work is group recommendation systems. Such a system embeds movies and users in the same feature space, and the task of recommending a movie for a group to watch together, translates to a set-query $ Q $ using an appropriate similarity.","PeriodicalId":447445,"journal":{"name":"Scandinavian Workshop on Algorithm Theory","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129633007","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: 1

Submodular Clustering in Low Dimensions 低维次模聚类

Scandinavian Workshop on Algorithm Theory Pub Date : 2020-04-11 DOI: 10.4230/LIPIcs.SWAT.2020.8

A. Backurs, Sariel Har-Peled

引用次数: 0

Simplifying Activity-on-Edge Graphs 简化边缘活动图

Scandinavian Workshop on Algorithm Theory Pub Date : 2020-02-05 DOI: 10.4230/LIPIcs.SWAT.2020.24

D. Eppstein, Daniel Frishberg, Elham Havvaei

引用次数: 0

Parameterized Complexity of Two-Interval Pattern Problem 双区间模式问题的参数化复杂度

Scandinavian Workshop on Algorithm Theory Pub Date : 2020-02-01 DOI: 10.4230/LIPIcs.SWAT.2020.16

P. Bose, S. Mehrabi, Debajyoti Mondal

{"title":"Parameterized Complexity of Two-Interval Pattern Problem","authors":"P. Bose, S. Mehrabi, Debajyoti Mondal","doi":"10.4230/LIPIcs.SWAT.2020.16","DOIUrl":"https://doi.org/10.4230/LIPIcs.SWAT.2020.16","url":null,"abstract":"A emph{2-interval} is the union of two disjoint intervals on the real line. Two 2-intervals $D_1$ and $D_2$ are emph{disjoint} if their intersection is empty (i.e., no interval of $D_1$ intersects any interval of $D_2$). There can be three different relations between two disjoint 2-intervals; namely, preceding ($<$), nested ($sqsubset$) and crossing ($between$). Two 2-intervals $D_1$ and $D_2$ are called emph{$R$-comparable} for some $Rin{<,sqsubset,between}$, if either $D_1RD_2$ or $D_2RD_1$. A set $mathcal{D}$ of disjoint 2-intervals is $mathcal{R}$-comparable, for some $mathcal{R}subseteq{<,sqsubset,between}$ and $mathcal{R}neqemptyset$, if every pair of 2-intervals in $mathcal{R}$ are $R$-comparable for some $Rinmathcal{R}$. Given a set of 2-intervals and some $mathcal{R}subseteq{<,sqsubset,between}$, the objective of the emph{2-interval pattern problem} is to find a largest subset of 2-intervals that is $mathcal{R}$-comparable. \u0000The 2-interval pattern problem is known to be $W[1]$-hard when $|mathcal{R}|=3$ and $NP$-hard when $|mathcal{R}|=2$ (except for $mathcal{R}={<,sqsubset}$, which is solvable in quadratic time). In this paper, we fully settle the parameterized complexity of the problem by showing it to be $W[1]$-hard for both $mathcal{R}={sqsubset,between}$ and $mathcal{R}={<,between}$ (when parameterized by the size of an optimal solution); this answers an open question posed by Vialette [Encyclopedia of Algorithms, 2008].","PeriodicalId":447445,"journal":{"name":"Scandinavian Workshop on Algorithm Theory","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128841096","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

Exact exponential algorithms for two poset problems 两个偏置集问题的精确指数算法

Scandinavian Workshop on Algorithm Theory Pub Date : 2019-12-30 DOI: 10.4230/LIPIcs.SWAT.2020.30

L. Kozma

{"title":"Exact exponential algorithms for two poset problems","authors":"L. Kozma","doi":"10.4230/LIPIcs.SWAT.2020.30","DOIUrl":"https://doi.org/10.4230/LIPIcs.SWAT.2020.30","url":null,"abstract":"Partially ordered sets (posets) are fundamental combinatorial objects with important applications in computer science. Perhaps the most natural algorithmic task, given a size-$n$ poset, is to compute its number of linear extensions. In 1991 Brightwell and Winkler showed this problem to be $#P$-hard. In spite of extensive research, the fastest known algorithm is still the straightforward $O(n 2^n)$-time dynamic programming (an adaptation of the Bellman-Held-Karp algorithm for the TSP). Very recently, Dittmer and Pak showed that the problem remains $#P$-hard for two-dimensional posets, and no algorithm was known to break the $2^n$-barrier even in this special case. The question of whether the two-dimensional problem is easier than the general case was raised decades ago by Mohring, Felsner and Wernisch, and others. In this paper we show that the number of linear extensions of a two-dimensional poset can be computed in time $O(1.8172^n)$. \u0000The related jump number problem asks for a linear extension of a poset, minimizing the number of neighboring incomparable pairs. The problem has applications in scheduling, and has been widely studied. In 1981 Pulleyblank showed it to be NP-complete. We show that the jump number problem can be solved (in arbitrary posets) in time $O(1.824^n)$. This improves (slightly) the previous best bound of Kratsch and Kratsch.","PeriodicalId":447445,"journal":{"name":"Scandinavian Workshop on Algorithm Theory","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125855678","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 Simple Algorithm for Minimum Cuts in Near-Linear Time 近线性时间最小切量的一种简单算法

Scandinavian Workshop on Algorithm Theory Pub Date : 2019-08-30 DOI: 10.4230/LIPIcs.SWAT.2020.12

Antonio Molina Lovett, Bryce Sandlund

引用次数: 14