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All reports by Author Thomas Thierauf:

TR17-127 | 12th August 2017
Rohit Gurjar, Thomas Thierauf, Nisheeth Vishnoi

Isolating a Vertex via Lattices: Polytopes with Totally Unimodular Faces

Revisions: 1

We deterministically construct quasi-polynomial weights in quasi-polynomial time, such that in a given polytope with totally unimodular constraints, one vertex is isolated, i.e., there is a unique minimum weight vertex.
More precisely,
the property that we need is that every face of the polytope lies in an affine space defined ... more >>>

TR16-182 | 14th November 2016
Rohit Gurjar, Thomas Thierauf

Linear Matroid Intersection is in quasi-NC

Given two matroids on the same ground set, the matroid intersection problem asks to find a common independent set of maximum size. We show that the linear matroid intersection problem is in quasi-NC$^2$. That is, it has uniform circuits of quasi-polynomial size $n^{O(\log n)}$, and $O(\log^2 n)$ depth. This generalizes ... more >>>

TR15-177 | 9th November 2015
Stephen A. Fenner, Rohit Gurjar, Thomas Thierauf

Bipartite Perfect Matching is in quasi-NC

Revisions: 2

We show that the bipartite perfect matching problem is in quasi-NC$^2$. That is, it has uniform circuits of quasi-polynomial size and $O(\log^2 n)$ depth. Previously, only an exponential upper bound was known on the size of such circuits with poly-logarithmic depth.

We obtain our result by an almost complete ... more >>>

TR15-021 | 5th February 2015
Stephen A. Fenner, Daniel Grier, Jochen Messner, Luke Schaeffer, Thomas Thierauf

Game Values and Computational Complexity: An Analysis via Black-White Combinatorial Games

A black-white combinatorial game is a two-person game in which the pieces are colored either black or white. The players alternate moving or taking elements of a specific color designated to them before the game begins. A player loses the game if there is no legal move available for his ... more >>>

TR14-158 | 26th November 2014
Rohit Gurjar, Arpita Korwar, Nitin Saxena, Thomas Thierauf

Deterministic Identity Testing for Sum of Read Once ABPs

Revisions: 2

A read once ABP is an arithmetic branching program with each variable occurring in at most one layer. We give the first polynomial time whitebox identity test for a polynomial computed by a sum of constantly many ROABPs. We also give a corresponding blackbox algorithm with quasi-polynomial time complexity, i.e. ... more >>>

TR14-079 | 11th June 2014
Simon Straub, Thomas Thierauf, Fabian Wagner

Counting the Number of Perfect Matchings in $K_5$-free Graphs

Counting the number of perfect matchings in arbitrary graphs is a $\#$P-complete problem. However, for some restricted classes of graphs the problem can be solved efficiently. In the case of planar graphs, and even for $K_{3,3}$-free graphs, Vazirani showed that it is in NC$^2$. The technique there is to compute ... more >>>

TR13-112 | 12th August 2013
Rohit Gurjar, Arpita Korwar, Jochen Messner, Thomas Thierauf

Exact Perfect Matching in Complete Graphs

A red-blue graph is a graph where every edge is colored either red or blue. The exact perfect matching problem asks for a perfect matching in a red-blue graph that has exactly a given number of red edges.

We show that for complete and bipartite complete graphs, the exact perfect ... more >>>

TR13-019 | 31st January 2013
Stephen A. Fenner, Rohit Gurjar, Arpita Korwar, Thomas Thierauf

On Two-Level Poset Games

We consider the complexity of determining the winner of a finite, two-level poset game.
This is a natural question, as it has been shown recently that determining the winner of a finite, three-level poset game is PSPACE-complete.
We give a simple formula allowing one to compute the status ... more >>>

TR11-148 | 3rd November 2011
Rohit Gurjar, Arpita Korwar, Jochen Messner, Simon Straub, Thomas Thierauf

Planarizing Gadgets for Perfect Matching do not Exist

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 >>>

TR11-018 | 8th February 2011
Jochen Messner, Thomas Thierauf

A Kolmogorov Complexity Proof of the Lovász Local Lemma for Satisfiability

Recently, Moser and Tardos [MT10] came up with a constructive proof of the Lovász Local Lemma. In this paper, we give another constructive proof of the lemma, based on Kolmogorov complexity. Actually, we even improve the Local Lemma slightly.

more >>>

TR10-050 | 25th March 2010
Samir Datta, Prajakta Nimbhorkar, Thomas Thierauf, Fabian Wagner

Graph Isomorphism for $K_{3,3}$-free and $K_5$-free graphs is in Log-space

Graph isomorphism is an important and widely studied computational problem, with
a yet unsettled complexity.
However, the exact complexity is known for isomorphism of various classes of
graphs. Recently [DLN$^+$09] proved that planar graph isomorphism is complete for log-space.
We extend this result of [DLN$^+$09] further
to the ... more >>>

TR09-052 | 2nd May 2009
Fabian Wagner, Samir Datta, Nutan Limaye, Prajakta Nimbhorkar, Thomas Thierauf

Planar Graph Isomorphism is in Log-space

Graph Isomorphism is the prime example of a computational problem with a wide difference between the best known lower and upper bounds on its complexity. There is a significant gap between extant lower and upper bounds for planar graphs as well. We bridge the gap for this natural and ... more >>>

TR09-029 | 3rd April 2009
Fabian Wagner, Thomas Thierauf

Reachability in K_{3,3}-free Graphs and K_5-free Graphs is in Unambiguous Log-Space

Revisions: 1

We show that the reachability problem for directed graphs
that are either K_{3,3}-free or K_5-free
is in unambiguous log-space, UL \cap coUL.
This significantly extends the result of Bourke, Tewari, and Vinodchandran
that the reachability problem for directed planar graphs
is in UL \cap coUL.

Our algorithm decomposes ... more >>>

TR07-068 | 24th July 2007
Thomas Thierauf, Fabian Wagner

The Isomorphism Problem for Planar 3-Connected Graphs is in Unambiguous Logspace

The isomorphism problem for planar graphs is known to be efficiently solvable. For planar 3-connected graphs, the isomorphism problem can be solved by efficient parallel algorithms, it is in the class AC^1.

In this paper we improve the upper bound for planar 3-connected graphs to unambiguous logspace, in fact to ... more >>>

TR06-129 | 6th October 2006
Manindra Agrawal, Thanh Minh Hoang, Thomas Thierauf

The polynomially bounded perfect matching problem is in NC^2

The perfect matching problem is known to
be in P, in randomized NC, and it is hard for NL.
Whether the perfect matching problem is in NC is one of
the most prominent open questions in complexity
theory regarding parallel computations.

Grigoriev and Karpinski studied the perfect matching problem
more >>>

TR04-024 | 26th March 2004
Thomas Thierauf, Thanh Minh Hoang

On Closure Properties of GapL

Revisions: 1 , Comments: 1

We show necessary and sufficient conditions that
certain algebraic functions like the rank or the signature
of an integer matrix can be computed in GapL.

more >>>

TR01-028 | 16th March 2001
Thanh Minh Hoang, Thomas Thierauf

The Complexity of the Minimal Polynomial

We investigate the computational complexity
of the minimal polynomial of an integer matrix.

We show that the computation of the minimal polynomial
is in AC^0(GapL), the AC^0-closure of the logspace
counting class GapL, which is contained in NC^2.
Our main result is that the problem is hard ... more >>>

TR97-060 | 2nd December 1997
Manindra Agrawal, Thomas Thierauf

The Satisfiability Problem for Probabilistic Ordered Branching Programs

We show that the satisfiability problem for
bounded error probabilistic ordered branching programs is NP-complete.
If the error is very small however
(more precisely,
if the error is bounded by the reciprocal of the width of the branching program),
then we have a polynomial-time algorithm for the satisfiability problem.
more >>>

TR96-040 | 21st May 1996
Thomas Thierauf

The Isomorphismproblem for One-Time-Only Branching Programs

Revisions: 1 , Comments: 1

We investigate the computational complexity of the
isomorphism problem for one-time-only branching programs (BP1-Iso):
on input of two one-time-only branching programs B and B',
decide whether there exists a permutation of the variables of B'
such that it becomes equivalent to B.

Our main result is a two-round interactive ... more >>>

TR96-032 | 12th March 1996
Manindra Agrawal, Thomas Thierauf

The Boolean Isomorphism Problem

We investigate the computational complexity of the Boolean Isomorphism problem (BI):
on input of two Boolean formulas F and G decide whether there exists a permutation of
the variables of G such that F and G become equivalent.

Our main result is a one-round interactive proof ... more >>>

TR96-001 | 10th January 1996
Manindra Agrawal, Richard Beigel, Thomas Thierauf

Modulo Information from Nonadaptive Queries to NP

The classes of languages accepted by nondeterministic polynomial-time
Turing machines (NP machines, in short) that have restricted access to
an NP oracle --- the machines can ask k queries to the NP oracle and
the answer they receive is the number of queries ... more >>>

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