Bounded Tree-Width and LOGCFL

An annotated bibliography on guaranteed graph searching

“…See [8,44,45,57,60,66,67,151,158,160,162] for results that were directly linked with search parameters. For results on graph searching on special graph classes, see [60,76,77,80,81,116,128,129,157,170].…”

Computing LOGCFL Certificates

“…• Deciding whether, for a ÿxed constant k, a graph G has treewidth 6k, i.e., whether a tree decomposition of width 6k for G exists [26].…”

“…The respective polynomial algorithms usually require the computation of a tree decomposition of bounded width. The following proposition summarizes important results by Wanke [26]. Proposition 5.2 (Wanke [26]).…”

Parallel algorithms with optimal speedup for bounded treewidth

“…Although these algorithms are fast, they are extremely wasteful in terms of processors, in view of the linear-time sequential algorithm. A related result was obtained by Wanke [41], who showed that the problem of deciding whether the treewidth of an input graph is bounded by a constant k belongs to the complexity dass LOGCFLj this result also does not seem to lead to parallel algorithms that are efficient from the point of view of processor utilization. If we relax the requirements by allowing tree decompositions of width O( k), rather than exactly k, more algorithms come into play: Lagergren [31] finds a decomposition of width ::::; 6k + 5 in O((1og n)3) time using n processors, and we believe that Reed's sequential O( n log n )-time algorithm [38] for obtaining a decomposition of width ::::; 4k + 3 can be parallelized (using an algorithm of Khuller and Schieber [29] to solve a central path-finding problem) to yield an algorithm that works in O( (log n )2) time using O( no:( n) flog n) processors, where 0: is a very slowly growing "inverse Ackermann" function.…”