Meena Mahajan, P R Subramanya, V Vinay

The Pfaffian of an oriented graph is closely linked to

Perfect Matching. It is also naturally related to the determinant of

an appropriately defined matrix. This relation between Pfaffian and

determinant is usually exploited to give a fast algorithm for

computing Pfaffians.

We present the first completely combinatorial algorithm for ... more >>>

Marek Karpinski, Miroslaw Kowaluk, Andrzej Lingas

The max-bisection problem is to find a partition of the vertices of a

graph into two equal size subsets that maximizes the number of edges with

endpoints in both subsets.

We obtain new improved approximation ratios for the max-bisection problem on

the low degree $k$-regular graphs for ...
more >>>

Klaus Jansen, Marek Karpinski, Andrzej Lingas

The Max-Bisection and Min-Bisection are the problems of finding

partitions of the vertices of a given graph into two equal size subsets so as

to maximize or minimize, respectively, the number of edges with exactly one

endpoint in each subset.

In this paper we design the first ...
more >>>

Eric Allender, Samir Datta, Sambuddha Roy

We investigate the s-t-connectivity problem for directed planar graphs, which is hard for L and is contained in NL but is not known to be complete. We show that this problem is logspace-reducible to its complement, and we show that the problem of searching graphs of genus 1 reduces to ... more >>>

Eric Allender, David Mix Barrington, Tanmoy Chakraborty, Samir Datta, Sambuddha Roy

We study the complexity of restricted versions of st-connectivity, which is the standard complete problem for NL. Grid graphs are a useful tool in this regard, since

* reachability on grid graphs is logspace-equivalent to reachability in general planar digraphs, and

* reachability on certain classes of grid graphs gives ...
more >>>

James R. Lee, Prasad Raghavendra

We show that the multi-commodity max-flow/min-cut gap for series-parallel graphs can be as bad as 2, matching a recent upper bound by Chakrabarti.et.al for this class, and resolving one side of a conjecture of Gupta, Newman, Rabinovich, and Sinclair.

This also improves the largest known gap for planar graphs ... more >>>

Raghav Kulkarni

The purpose of this paper is to study the deterministic

{\em isolation} for certain structures in directed and undirected

planar graphs.

The motivation behind this work is a recent development on this topic. For example, \cite{btv07} isolate a directed path in planar graphs and

\cite{dkr08} isolate a perfect matching in ...
more >>>

Rohit Gurjar, Arpita Korwar, Jochen Messner, Simon Straub, Thomas Thierauf

To compare the complexity of the perfect matching problem for general graphs with that for planar graphs, one might try to come up with a reduction from the perfect matching problem to the planar perfect matching problem.

The obvious way to construct such a reduction is via a {\em planarizing ...
more >>>

Kshitij Gajjar, Jaikumar Radhakrishnan

We construct a family of planar graphs $(G_n: n\geq 4)$, where $G_n$ has $n$ vertices including a source vertex $s$ and a sink vertex $t$, and edge weights that change linearly with a parameter $\lambda$ such that, as $\lambda$ increases, the cost of the shortest path from $s$ to $t$ ... more >>>