Abstract
Elkin, Emek, Spielman and Teng showed recently that every graph can be
probabilistically embedded into a distribution over its spanning trees with
polylogarithmic expected distortion, narrowing the gap left by Alon, Karp, Peleg and
West that established a logarithmic lower bound in 1995. This lower bound holds
even
for the class of series-parallel graphs as Gupta, Newman, Rabinovich and Sinclair
.proved in 1999
In this work we close this gap for series-parallel graphs, namely, we prove that every
n$-vertex series-parallel graph can be probabilistically embedded into a distribution$
over its spanning trees with expected stretch $O(\log{n})$ for every two vertices. We
gain our upper bound by presenting a polynomial time probabilistic algorithm that
constructs spanning trees with low expected stretch. This probabilistic algorithm can
be derandomized to yield a deterministic polynomial time algorithm for constructing a
spanning tree of a given series-parallel graph $G$, whose communication cost is at
most $O(\log{n})$ times larger than that of $ G
Bio
Yuval is a Ph.D. student at the Department of Computer Science and Applied
Mathematics
in the Weizmann Institute of Science. His fields of interest include combinatorial
optimization, graph theory and coping with NP-hardness. He is conducting his
research
under the advice of Prof. David Peleg. Yuval has a B.A. in computer science from the
Technion (summa cum laude) and an M.Sc. from the Weizmann Institute of Science.
He is
.on the Feinberg Graduate School Dean's list of honor for 2005
.