Linear-time computation of optimal subgraphs of decomposable graphs
Journal of Algorithms
Binary tree algebraic computation and parallel algorithms for simple graphs
Journal of Algorithms
Linear time algorithms for NP-hard problems restricted to partial k-trees
Discrete Applied Mathematics
A simple parallel tree contraction algorithm
Journal of Algorithms
Efficient parallel algorithms for series parallel graphs
Journal of Algorithms
Parallel algorithms for shared-memory machines
Handbook of theoretical computer science (vol. A)
An introduction to parallel algorithms
An introduction to parallel algorithms
Regularity and locality in k-terminal graphs
Discrete Applied Mathematics - Special issue: efficient algorithms and partial k-trees
Linear-time computability of combinatorial problems on series-parallel graphs
Journal of the ACM (JACM)
Characterization of Efficiently Parallel Solvable Problems on Distance-Hereditary Graphs
SIAM Journal on Discrete Mathematics
Linear algorithms on k-terminal graphs
Linear algorithms on k-terminal graphs
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
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In the literature, there are quite a few sequential and parallel algorithms to solve problems on decomposable graphs utilizing distinct techniques. Trees, series-parallel graphs, outerplanar graphs, and bandwidth-k graphs all belong to decomposable graphs. Let Td(|V|,|E|) and Pd (|V|,|E|) denote the time complexity and processor complexity required to construct a parse tree representation TG for a decomposable graph G = (V, E) on a PRAM model Md. We define a general problem-solving paradigm to solve a wide class of subgraph optimization problems on decomposable graphs in O(Td(|V|,|E|)+log|V(TG)|) time using O(Pd(|V|, |E|) + |V(TG)|/log|V(TG|) processors on Md. We also demonstrate the following examples fitting into our paradigm: (1) The maximum independent set problem on trees, (2) The maximum matching problem on series-parallel graphs, and (3) The efficient domination problem on series-parallel graphs. Our results improve the previously best known results of (1) and (2).