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REPORTS > KEYWORD > TREEWIDTH:
Reports tagged with Treewidth:
TR97-041 | 18th September 1997
Marek Karpinski, Juergen Wirtgen

#### On Approximation Hardness of the Bandwidth Problem

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 >>>

TR12-027 | 29th March 2012
Eric Allender, Shiteng Chen, Tiancheng Lou, Periklis Papakonstantinou, Bangsheng Tang

#### Time-space tradeoffs for width-parameterized SAT:Algorithms and lower bounds

Revisions: 2

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 >>>

TR12-126 | 23rd September 2012
Shiva Kintali, Sinziana Munteanu

#### Computing Bounded Path Decompositions in Logspace

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 >>>

TR13-113 | 19th August 2013
Moritz Müller, Stefan Szeider

#### Revisiting Space in Proof Complexity: Treewidth and Pathwidth

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 >>>

TR18-004 | 3rd January 2018
Aayush Ojha, Raghunath Tewari

#### Circuit Complexity of Bounded Planar Cutwidth Graph Matching

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 >>>

TR19-020 | 4th February 2019
Ludmila Glinskih, Dmitry Itsykson

#### On Tseitin formulas, read-once branching programs and treewidth

Revisions: 1

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 >>>

TR19-178 | 5th December 2019
Dmitry Itsykson, Artur Riazanov, Danil Sagunov, Petr Smirnov

#### Almost Tight Lower Bounds on Regular Resolution Refutations of Tseitin Formulas for All Constant-Degree Graphs

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 >>>

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