We present a new technique for constructing and analyzing couplings to bound the convergence rate of finite Markov chains. Our main theorem is a generalization of the path couplin...
1 The Ramsey number R(G1, G2) is the smallest integer p such that for any graph G on p vertices2 either G contains G1 or G contains G2, where G denotes the complement of G. In this...
We consider the reachability problem for a certain class of directed acyclic graphs embedded on surfaces. Let G(m, g) be the class of directed acyclic graphs with m = m(n) source ...
— While the practical coding scheme [1] has been shown to be able to improve throughput of wireless networks, there still lacks fundamental understanding on how the coding scheme...
Many instances of NP-hard problems can be solved efficiently if the treewidth of their corresponding graph is small. Finding the optimal tree decompositions is an NP-hard problem a...