Parameterized Streaming Algorithms for Vertex Cover release_4mqzunoomvdahi3kbssuvf7cjy

by Rajesh Chitnis, Graham Cormode, MohammadTaghi Hajiaghayi, Morteza Monemizadeh

Released as a article .

2014  

Abstract

As graphs continue to grow in size, we seek ways to effectively process such data at scale. The model of streaming graph processing, in which a compact summary is maintained as each edge insertion/deletion is observed, is an attractive one. However, few results are known for optimization problems over such dynamic graph streams. In this paper, we introduce a new approach to handling graph streams, by instead seeking solutions for the parameterized versions of these problems where we are given a parameter k and the objective is to decide whether there is a solution bounded by k. By combining kernelization techniques with randomized sketch structures, we obtain the first streaming algorithms for the parameterized versions of the Vertex Cover problem. We consider the following three models for a graph stream on n nodes: 1. The insertion-only model where the edges can only be added. 2. The dynamic model where edges can be both inserted and deleted. 3. The promised dynamic model where we are guaranteed that at each timestamp there is a solution of size at most k. In each of these three models we are able to design parameterized streaming algorithms for the Vertex Cover problem. We are also able to show matching lower bound for the space complexity of our algorithms. (Due to the arXiv limit of 1920 characters for abstract field, please see the abstract in the paper for detailed description of our results)
In text/plain format

Archived Files and Locations

application/pdf  367.7 kB
file_wxn7whs2bvafll7xf6f2w5tczy
arxiv.org (repository)
web.archive.org (webarchive)
Read Archived PDF
Preserved and Accessible
Type  article
Stage   submitted
Date   2014-07-23
Version   v2
Language   en ?
arXiv  1405.0093v2
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: 1566d643-6a4c-4e49-8bc7-c73f06d8cd9c
API URL: JSON