Approximating Upper Degree-Constrained Partial Orientations

In the Upper Degree-Constrained Partial Orientation (UDPO) problem we are given an undirected graph G = (V, E), together with two degree constraint functions d− , d+ : V → N. The goal is to orient as many edges as possible, in such a way that for each vertex v ∈ V the number of arcs entering v is at most d− (v), whereas the number of arcs leaving v is at most d+ (v). This problem was introduced by Gabow [SODA’06], who proved it to be MAXSNP-hard (and thus APX-hard). In the same paper Gabow presented an LP-based iterative rounding 4/3-approximation algorithm. As already observed by Gabow, the problem in question is a special case of the classic 3Dimensional Matching, which in turn is a special case of the k-Set Packing problem. Back in 2006 the best known polynomial time approximation algorithm for 3-Dimensional Matching was a simple local search by Hurkens and Schrijver [SIDMA’89], the approximation ratio of which is (3 + ε)/2; hence the algorithm of Gabow was an improvem...

• Type: Journal
• Year: 2015
• Where: APPROX
• Authors: Marek Cygan, Tomasz Kociumaka
• Keywords: Algorithms, APPROX 2015