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Electronic Colloquium on Computational Complexity

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Reports tagged with graph:
TR05-153 | 9th December 2005
Shirley Halevy, Oded Lachish, Ilan Newman, Dekel Tsur

Testing Orientation Properties

We propose a new model for studying graph related problems
that we call the \emph{orientation model}. In this model, an undirected
graph $G$ is fixed, and the input is any possible edge orientation
of $G$. A property is now a property of the directed graph that is
obtained by a ... more >>>

TR08-110 | 19th November 2008
Chris Calabro

A Lower Bound on the Size of Series-Parallel Graphs Dense in Long Paths

One way to quantify how dense a multidag is in long paths is to find
the largest n, m such that whichever ≤ n edges are removed, there is still
a path from an original input to an original output with ≥ m edges
- the larger ... more >>>

TR09-049 | 5th May 2009
Derrick Stolee, Chris Bourke, N. V. Vinodchandran

A log-space algorithm for reachability in planar DAGs with few sources

Designing algorithms that use logarithmic space for graph reachability problems is fundamental to complexity theory. It is well known that for general directed graphs this problem is equivalent to the NL vs L problem. For planar graphs, the question is not settled. Showing that the planar reachability problem is NL-complete ... more >>>

TR13-012 | 16th January 2013
Hasan Abasi, Nader Bshouty

A Simple Algorithm for Undirected Hamiltonicity

We develop a new algebraic technique that gives a simple randomized algorithm for the simple $k$-path problem with the same complexity $O^*(1.657^k)$ as in [A. Bj\"orklund. Determinant Sums for Undirected Hamiltonicity. FOCS 2010, pp. 173--182, (2010). A. Bj\"orklund, T. Husfeldt, P. Kaski, M. Koivisto. Narrow sieves for parameterized paths and ... more >>>

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