TY - GEN

T1 - Algorithms and hardness for signed domination

AU - Lin, Jin Yong

AU - Poon, Sheung Hung

N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2015.

PY - 2015

Y1 - 2015

N2 - A signed dominating function for a graph G = (V,E) is a function f: V → {+1,−1} such that for all v ∈ V, the sum of the function values over the closed neighborhood of v is at least one. The weight w(f(V)) of signed dominating function f for vertex set V is the sum of f(v) for v ∈ V. The signed domination number γs of G is the minimum weight of a signed dominating function for G. The signed domination (SD) problem asks for a signed dominating function which contributes the signed domination number. First we show that the SD problem is W[2]-hard. Next we show that the SD problem on graphs of maximum degree six is APX-hard. Then we present constant-factor approximation algorithms for the SD problem on subcubic graphs, graphs of maximum degree four, and graphs of maximum degree five, respectively. In addition, we present an alternative and more direct proof for the NP-completeness of the SD problem on subcubic planar bipartite graphs. Lastly, we obtain an O∗ (5.1957k)-time FPT-algorithm for the SD problem on subcubic graphs G, where k is the signed domination number of G.

AB - A signed dominating function for a graph G = (V,E) is a function f: V → {+1,−1} such that for all v ∈ V, the sum of the function values over the closed neighborhood of v is at least one. The weight w(f(V)) of signed dominating function f for vertex set V is the sum of f(v) for v ∈ V. The signed domination number γs of G is the minimum weight of a signed dominating function for G. The signed domination (SD) problem asks for a signed dominating function which contributes the signed domination number. First we show that the SD problem is W[2]-hard. Next we show that the SD problem on graphs of maximum degree six is APX-hard. Then we present constant-factor approximation algorithms for the SD problem on subcubic graphs, graphs of maximum degree four, and graphs of maximum degree five, respectively. In addition, we present an alternative and more direct proof for the NP-completeness of the SD problem on subcubic planar bipartite graphs. Lastly, we obtain an O∗ (5.1957k)-time FPT-algorithm for the SD problem on subcubic graphs G, where k is the signed domination number of G.

UR - http://www.scopus.com/inward/record.url?scp=84929629914&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-17142-5_38

DO - 10.1007/978-3-319-17142-5_38

M3 - Conference contribution

AN - SCOPUS:84929629914

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 453

EP - 464

BT - Theory and Applications of Models of Computation - 12th Annual Conference, TAMC 2015, Proceedings

A2 - Jain, Rahul

A2 - Jain, Sanjay

A2 - Stephan, Frank

PB - Springer Verlag

T2 - 12th Annual Conference on Theory and Applications of Models of Computation, TAMC 2015

Y2 - 18 May 2015 through 20 May 2015

ER -