Scandinavian Workshop on Algorithm Theory最新文献_第5页

Extension Complexity, MSO Logic, and Treewidth 扩展复杂度，MSO逻辑和树宽度

Scandinavian Workshop on Algorithm Theory Pub Date : 2015-07-17 DOI: 10.23638/DMTCS-22-4-8

P. Kolman, Martin Koutecký, Hans Raj Tiwary

{"title":"Extension Complexity, MSO Logic, and Treewidth","authors":"P. Kolman, Martin Koutecký, Hans Raj Tiwary","doi":"10.23638/DMTCS-22-4-8","DOIUrl":"https://doi.org/10.23638/DMTCS-22-4-8","url":null,"abstract":"We consider the convex hull $P_{varphi}(G)$ of all satisfying assignments of a given MSO formula $varphi$ on a given graph $G$. We show that there exists an extended formulation of the polytope $P_{varphi}(G)$ that can be described by $f(|varphi|,tau)cdot n$ inequalities, where $n$ is the number of vertices in $G$, $tau$ is the treewidth of $G$ and $f$ is a computable function depending only on $varphi$ and $tau.$ \u0000In other words, we prove that the extension complexity of $P_{varphi}(G)$ is linear in the size of the graph $G$, with a constant depending on the treewidth of $G$ and the formula $varphi$. This provides a very general yet very simple meta-theorem about the extension complexity of polytopes related to a wide class of problems and graphs. As a corollary of our main result, we obtain an analogous result % for the weaker MSO$_1$ logic on the wider class of graphs of bounded cliquewidth. \u0000Furthermore, we study our main geometric tool which we term the glued product of polytopes. While the glued product of polytopes has been known since the '90s, we are the first to show that it preserves decomposability and boundedness of treewidth of the constraint matrix. This implies that our extension of $P_varphi(G)$ is decomposable and has a constraint matrix of bounded treewidth; so far only few classes of polytopes are known to be decomposable. These properties make our extension useful in the construction of algorithms.","PeriodicalId":447445,"journal":{"name":"Scandinavian Workshop on Algorithm Theory","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127716382","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: 20

Coloring Graphs Having Few Colorings Over Path Decompositions 在路径分解上具有很少着色的着色图

Scandinavian Workshop on Algorithm Theory Pub Date : 2015-04-14 DOI: 10.4230/LIPIcs.SWAT.2016.13

Andreas Björklund

{"title":"Coloring Graphs Having Few Colorings Over Path Decompositions","authors":"Andreas Björklund","doi":"10.4230/LIPIcs.SWAT.2016.13","DOIUrl":"https://doi.org/10.4230/LIPIcs.SWAT.2016.13","url":null,"abstract":"Lokshtanov, Marx, and Saurabh SODA 2011 proved that there is no (k-epsilon)^pw(G)poly(n) time algorithm for deciding if an n-vertex graph G with pathwidth pw admits a proper vertex coloring with k colors unless the Strong Exponential Time Hypothesis (SETH) is false, for any constant epsilon>0. We show here that nevertheless, when k>lfloor Delta/2 rfloor + 1, where Delta is the maximum degree in the graph G, there is a better algorithm, at least when there are few colorings. We present a Monte Carlo algorithm that given a graph G along with a path decomposition of G with pathwidth pw(G) runs in (lfloor Delta/2 rfloor + 1)^pw(G)poly(n)s time, that distinguishes between k-colorable graphs having at most s proper k-colorings and non-k-colorable graphs. We also show how to obtain a k-coloring in the same asymptotic running time. Our algorithm avoids violating SETH for one since high degree vertices still cost too much and the mentioned hardness construction uses a lot of them. \u0000 \u0000We exploit a new variation of the famous Alon--Tarsi theorem that has an algorithmic advantage over the original form. The original theorem shows a graph has an orientation with outdegree less than k at every vertex, with a different number of odd and even Eulerian subgraphs only if the graph is k-colorable, but there is no known way of efficiently finding such an orientation. Our new form shows that if we instead count another difference of even and odd subgraphs meeting modular degree constraints at every vertex picked uniformly at random, we have a fair chance of getting a non-zero value if the graph has few k-colorings. Yet every non-k-colorable graph gives a zero difference, so a random set of constraints stands a good chance of being useful for separating the two cases.","PeriodicalId":447445,"journal":{"name":"Scandinavian Workshop on Algorithm Theory","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114902199","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

I/O-Efficient Range Minima Queries I/ o高效范围最小化查询

Scandinavian Workshop on Algorithm Theory Pub Date : 2014-07-02 DOI: 10.1007/978-3-319-08404-6_1

P. Afshani, Nodari Sitchinava

引用次数: 5

Minimum Tree Supports for Hypergraphs and Low-Concurrency Euler Diagrams 最小树支持超图和低并发欧拉图

Scandinavian Workshop on Algorithm Theory Pub Date : 2014-07-02 DOI: 10.1007/978-3-319-08404-6_23

Boris Klemz, T. Mchedlidze, M. Nöllenburg

引用次数: 17

B-slack Trees: Space Efficient B-Trees b -松弛树:空间高效的b -树

Scandinavian Workshop on Algorithm Theory Pub Date : 2014-07-02 DOI: 10.1007/978-3-319-08404-6_11

Trevor Brown

引用次数: 7

Competitive Online Routing on Delaunay Triangulations 基于Delaunay三角的竞争在线路由

Scandinavian Workshop on Algorithm Theory Pub Date : 2014-07-02 DOI: 10.1007/978-3-319-08404-6_9

P. Bose, J. Carufel, Stephane Durocher, Perouz Taslakian

引用次数: 14

Colored Range Searching in Linear Space 线性空间中的彩色范围搜索

Scandinavian Workshop on Algorithm Theory Pub Date : 2014-07-02 DOI: 10.1007/978-3-319-08404-6_20

R. Grossi, Søren Vind

引用次数: 7

On Matchings and b-Edge Dominating Sets: A 2-Approximation Algorithm for the 3-Edge Dominating Set Problem 关于匹配和b边控制集:3边控制集问题的2-逼近算法

Scandinavian Workshop on Algorithm Theory Pub Date : 2014-07-02 DOI: 10.1007/978-3-319-08404-6_18

Toshihiro Fujito

引用次数: 4

Expected Linear Time Sorting for Word Size Ω(log2 n loglogn) 单词大小的期望线性时间排序Ω(log2 n loglog)

Scandinavian Workshop on Algorithm Theory Pub Date : 2014-07-02 DOI: 10.1007/978-3-319-08404-6_3

D. Belazzougui, G. Brodal, J. Nielsen

引用次数: 7

Approximation Algorithms for Hitting Triangle-Free Sets of Line Segments 触及无三角线段集的逼近算法

Scandinavian Workshop on Algorithm Theory Pub Date : 2014-07-02 DOI: 10.1007/978-3-319-08404-6_31

Anup Joshi, N. Narayanaswamy

引用次数: 2