TY - GEN
T1 - Approximation algorithms for the graph orientation minimizing the maximum weighted outdegree
AU - Asahiro, Yuichi
AU - Jansson, Jesper Andreas
AU - Miyano, Eiji
AU - Ono, Hirotaka
AU - Zenmyo, Kouhei
PY - 2007/12/1
Y1 - 2007/12/1
N2 - Given an undirected graph G = (V, E) and a weight function w : E → ℤ+, we consider the problem of orienting all edges in E so that the maximum weighted outdegree among all vertices is minimized. In this paper (1) we prove that the problem is strongly NP-hard if all edge weights belong to the set {1 ,k}, where k is any 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 polynomial time algorithm that approximates the general version of the problem within a factor 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 factor of 3/2 for k = 2 (note that this matches the inapproximability bound above), and (2 - 2/(k + 1)) for any k ≥ 3, respectively, in polynomial time.
AB - Given an undirected graph G = (V, E) and a weight function w : E → ℤ+, we consider the problem of orienting all edges in E so that the maximum weighted outdegree among all vertices is minimized. In this paper (1) we prove that the problem is strongly NP-hard if all edge weights belong to the set {1 ,k}, where k is any 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 polynomial time algorithm that approximates the general version of the problem within a factor 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 factor of 3/2 for k = 2 (note that this matches the inapproximability bound above), and (2 - 2/(k + 1)) for any k ≥ 3, respectively, in polynomial time.
UR - http://www.scopus.com/inward/record.url?scp=38149071598&partnerID=8YFLogxK
M3 - Conference article published in proceeding or book
SN - 9783540728689
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 167
EP - 177
BT - Algorithmic Aspects in Information and Management - Third International Conference, AAIM 2007, Proceedings
T2 - 3rd International Conference on Algorithmic Aspects in Information and Management, AAIM 2007
Y2 - 6 June 2007 through 8 June 2007
ER -