The bandwidth problem is the problem of enumerating
the vertices of a given graph $G$ such that the maximum
difference between the numbers of
adjacent vertices is minimal. The problem has a long
history and a number of applications
and is ... more >>>

A decade has passed since Alekhnovich and Razborov presented an algorithm that solves SAT on instances $\phi$ of size $n$ having tree-width $TW(\phi)$, using time (and space) bounded by $2^{O(TW(\phi))}n^{O(1)}$. Although there have been several papers over the ensuing years building on the work of Alekhnovich and Razborov there has ... more >>>

We present a logspace algorithm to compute path decompositions of bounded pathwidth graphs, thus settling its complexity. Prior to our work, the best known upper bound to compute such decompositions was linear time. We also show that deciding if the pathwidth of a graph is at most a given constant ... more >>>

So-called ordered variants of the classical notions of pathwidth and treewidth are introduced and proposed as proof theoretically meaningful complexity measures for the directed acyclic graphs underlying proofs. The ordered pathwidth of a proof is shown to be roughly the same as its formula space. Length-space lower bounds for R(k)-refutations ... more >>>

Recently, perfect matching in bounded planar cutwidth bipartite graphs
$BGGM$ was shown to be in ACC$^0$ by Hansen et al.. They also conjectured that
the problem is in AC$^0$.
In this paper, we disprove their conjecture by showing that the problem is
not in AC$^0[p^{\alpha}]$ for every prime $p$. ... more >>>

We show that any nondeterministic read-once branching program that computes a satisfiable Tseitin formula based on an $n\times n$ grid graph has size at least $2^{\Omega(n)}$. Then using the Excluded Grid Theorem by Robertson and Seymour we show that for arbitrary graph $G(V,E)$ any nondeterministic read-once branching program that computes ... more >>>

We show that the size of any regular resolution refutation of Tseitin formula $T(G,c)$ based on a graph $G$ is at least $2^{\Omega(tw(G)/\log n)}$, where $n$ is the number of vertices in $G$ and $tw(G)$ is the treewidth of $G$. For constant degree graphs there is known upper bound $2^{O(tw(G))}$ ... more >>>

In this paper, we establish a novel connection between total variation (TV) distance estimation and probabilistic inference. In particular, we present an efficient, structure-preserving reduction from relative approximation of TV distance to probabilistic inference over directed graphical models. This reduction leads to a fully polynomial randomized approximation scheme (FPRAS) for ... more >>>

In this paper we study syntactic branching programs of bounded repetition
representing CNFs of bounded treewidth.
For this purpose we introduce two new structural graph
parameters $d$-pathwidth and clique preserving $d$-pathwidth denoted
by $pw_d(G)$ and $cpw_d(G)$ where $G$ is a graph.
We show that $cpw_2(G) \leq O(tw(G) \Delta(G))$ ... more >>>