7 research outputs found
Space Complexity of Perfect Matching in Bounded Genus Bipartite Graphs
We investigate the space complexity of certain perfect matching problems over
bipartite graphs embedded on surfaces of constant genus (orientable or
non-orientable). We show that the problems of deciding whether such graphs have
(1) a perfect matching or not and (2) a unique perfect matching or not, are in
the logspace complexity class \SPL. Since \SPL\ is contained in the logspace
counting classes \oplus\L (in fact in \modk\ for all ), \CeqL, and
\PL, our upper bound places the above-mentioned matching problems in these
counting classes as well. We also show that the search version, computing a
perfect matching, for this class of graphs is in \FL^{\SPL}. Our results
extend the same upper bounds for these problems over bipartite planar graphs
known earlier. As our main technical result, we design a logspace computable
and polynomially bounded weight function which isolates a minimum weight
perfect matching in bipartite graphs embedded on surfaces of constant genus. We
use results from algebraic topology for proving the correctness of the weight
function.Comment: 23 pages, 13 figure
Trading Determinism for Time in Space Bounded Computations
Savitch showed in that nondeterministic logspace (NL) is contained in
deterministic space but his algorithm requires
quasipolynomial time. The question whether we can have a deterministic
algorithm for every problem in NL that requires polylogarithmic space and
simultaneously runs in polynomial time was left open.
In this paper we give a partial solution to this problem and show that for
every language in NL there exists an unambiguous nondeterministic algorithm
that requires space and simultaneously runs in
polynomial time.Comment: Accepted in MFCS 201