TY - JOUR
T1 - Polynomial-time data reduction for the subset interconnection design problem
AU - Chen, Jiehua
AU - Komusiewicz, Christian
AU - Niedermeier, Rolf
AU - Sorge, Manuel
AU - Suchy, Ondřej
AU - Weller, Mathias
N1 - Publisher Copyright:
© 2015 Society for Industrial and Applied Mathematics.
PY - 2015/1/1
Y1 - 2015/1/1
N2 - The NP-hard SUBSET INTERCONNECTION DESIGN problem, also known as MINIMUM TOPIC-CONNECTED OVERLAY, is motivated by numerous applications including the design of scalable overlay networks and vacuum systems. It has as input a finite set V and a collection of subsets V1, V2, . . ., Vm ⊆ V, and asks for a minimum-cardinality edge set E such that for the graph G = (V, E) all induced subgraphs G[V1], G[V2], . . ., G[Vm] are connected. We study SUBSET INTERCONNECTION DESIGN in the context of polynomial-time data reduction rules that preserve the possibility of constructing optimal solutions. Our contribution is threefold: First, we show the incorrectness of earlier polynomial-time data reduction rules. Second, we show linear-time solvability in case of a constant number m of subsets, implying fixed-parameter tractability for the parameter m. Third, we provide a fixed-parameter tractability result for small subset sizes and tree-like output graphs. To achieve our results, we elaborate on polynomial-time data reduction rules which also may be of practical use in solving Subset Interconnection Design.
AB - The NP-hard SUBSET INTERCONNECTION DESIGN problem, also known as MINIMUM TOPIC-CONNECTED OVERLAY, is motivated by numerous applications including the design of scalable overlay networks and vacuum systems. It has as input a finite set V and a collection of subsets V1, V2, . . ., Vm ⊆ V, and asks for a minimum-cardinality edge set E such that for the graph G = (V, E) all induced subgraphs G[V1], G[V2], . . ., G[Vm] are connected. We study SUBSET INTERCONNECTION DESIGN in the context of polynomial-time data reduction rules that preserve the possibility of constructing optimal solutions. Our contribution is threefold: First, we show the incorrectness of earlier polynomial-time data reduction rules. Second, we show linear-time solvability in case of a constant number m of subsets, implying fixed-parameter tractability for the parameter m. Third, we provide a fixed-parameter tractability result for small subset sizes and tree-like output graphs. To achieve our results, we elaborate on polynomial-time data reduction rules which also may be of practical use in solving Subset Interconnection Design.
KW - Combinatorial algorithms
KW - Fixed-parameter tractability
KW - Hypergraph support
KW - Kernelization
KW - NP-hard problem
KW - Preprocessing
UR - http://www.scopus.com/inward/record.url?scp=84925362645&partnerID=8YFLogxK
U2 - 10.1137/140955057
DO - 10.1137/140955057
M3 - Article
AN - SCOPUS:84925362645
SN - 0895-4801
VL - 29
SP - 1
EP - 25
JO - SIAM Journal on Discrete Mathematics
JF - SIAM Journal on Discrete Mathematics
IS - 1
ER -