TY - GEN
T1 - Degree-constrained graph orientation: Maximum satisfaction and minimum violation
AU - Asahiro, Yuichi
AU - Jansson, Jesper Andreas
AU - Miyano, Eiji
AU - Ono, Hirotaka
PY - 2013/1/1
Y1 - 2013/1/1
N2 - A degree-constrained graph orientation of an undirected graph G is an assignment of a direction to each edge in G such that the outdegree of every vertex in the resulting directed graph satisfies a specified lower and/or upper bound. Such graph orientations have been studied for a long time and various characterizations of their existence are known. In this paper, we consider four related optimization problems introduced in [4]: For any fixed non-negative integer W, the problems Max W -Light, Min W -Light, Max W -Heavy, and Min W -Heavy take as input an undirected graph G and ask for an orientation of G that maximizes or minimizes the number of vertices with outdegree at most W or at least W. The problems' computational complexities vary with W. Here, we resolve several open questions related to their polynomial-time approximability and present a number of positive and negative results.
AB - A degree-constrained graph orientation of an undirected graph G is an assignment of a direction to each edge in G such that the outdegree of every vertex in the resulting directed graph satisfies a specified lower and/or upper bound. Such graph orientations have been studied for a long time and various characterizations of their existence are known. In this paper, we consider four related optimization problems introduced in [4]: For any fixed non-negative integer W, the problems Max W -Light, Min W -Light, Max W -Heavy, and Min W -Heavy take as input an undirected graph G and ask for an orientation of G that maximizes or minimizes the number of vertices with outdegree at most W or at least W. The problems' computational complexities vary with W. Here, we resolve several open questions related to their polynomial-time approximability and present a number of positive and negative results.
UR - http://www.scopus.com/inward/record.url?scp=84903631659&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-08001-7_3
DO - 10.1007/978-3-319-08001-7_3
M3 - Conference article published in proceeding or book
SN - 9783319080000
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 24
EP - 36
BT - Approximation and Online Algorithms - 11th International Workshop, WAOA 2013, Revised Selected Papers
PB - Springer Verlag
T2 - 11th International Workshop on Approximation and Online Algorithms, WAOA 2013
Y2 - 5 September 2013 through 6 September 2013
ER -