Approximation algorithms for the graph orientation minimizing the maximum weighted outdegree

作     者：Asahiro, Yuichi Jansson, Jesper Miyano, Eiji Ono, Hirotaka Zenmyo, Kouhei 

作者机构：Kyushu Univ Dept Informat Nishi Ku Fukuoka 8190395 Japan Kyushu Sangyo Univ Dept Informat Sci Higashi Ku Fukuoka 8138503 Japan Ochanomizu Univ Bunkyo Ku Tokyo 1128610 Japan Kyushu Inst Technol Dept Syst Design & Informat Fukuoka 8508502 Japan 

出 版 物：《JOURNAL OF COMBINATORIAL OPTIMIZATION》 (组合优化杂志)

年 卷 期：2011年第22卷第1期

页      面：78-96页

核心收录：

学科分类：12[管理学] 120202[管理学-企业管理（含：财务管理、市场营销、人力资源管理）] 0202[经济学-应用经济学] 02[经济学] 1202[管理学-工商管理] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：KAKENHI [16092223, 17700022, 18700015, 20500017, 21680001] Asahi glass foundation Inamori foundation Grants-in-Aid for Scientific Research [16092223, 20500017, 17700022, 21680001, 23500020, 18700015, 22700019] Funding Source: KAKEN 

主　　题：Graph orientation Degree Approximation algorithm Inapproximability Maximum flow Scheduling 

摘      要：Given a simple, undirected graph G=(V,E) and a weight function w:E - acurrency sign(+), we consider the problem of orienting all edges in E so that the maximum weighted outdegree among all vertices is minimized. It has previously been shown that the unweighted version of the problem is solvable in polynomial time while the weighted version is (weakly) NP-hard. In this paper, we strengthen these results as follows: (1) We prove that the weighted version is strongly NP-hard even if all edge weights belong to the set {1,k}, where k is any fixed integer greater than or equal to 2, and that there exists no pseudo-polynomial time approximation algorithm for this problem whose approximation ratio is smaller than (1+1/k) unless P = NP;(2) we present a new polynomial-time algorithm that approximates the general version of the problem within a ratio of (2-1/k), where k is the maximum weight of an edge in G;(3) we show how to approximate the special case in which all edge weights belong to {1,k} within a ratio of 3/2 for k=2 (note that this matches the inapproximability bound above), and (2-2/(k+1)) for any ka parts per thousand yen3, respectively, in polynomial time.