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Electronic Colloquium on Computational Complexity

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REPORTS > AUTHORS > FABIAN WAGNER:
All reports by Author Fabian Wagner:

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 >>>


TR11-052 | 4th April 2011
Fabian Wagner

On the Complexity of Group Isomorphism

Revisions: 4 , Comments: 3

The group isomorphism problem consists in deciding whether two groups $G$ and $H$
given by their multiplication tables are isomorphic.
An algorithm for group isomorphism attributed to Tarjan runs in time $n^{\log n + O(1)}$, c.f. [Mil78].

Miller and Monk showed in [Mil79] that group isomorphism can be many-one ... more >>>


TR11-032 | 11th March 2011
Fabian Wagner

Graphs of Bounded Treewidth can be Canonized in AC$^1$

In recent results the complexity of isomorphism testing on
graphs of bounded treewidth is improved to TC$^1$ [GV06] and further to LogCFL [DTW10].
The computation of canonical forms or a canonical labeling provides more information than
isomorphism testing.
Whether canonization is in NC or even TC$^1$ was stated ... more >>>


TR10-117 | 22nd July 2010
Arkadev Chattopadhyay, Jacobo Toran, Fabian Wagner

Graph Isomorphism is not AC^0 reducible to Group Isomorphism

We give a new upper bound for the Group and Quasigroup
Isomorphism problems when the input structures
are given explicitly by multiplication tables. We show that these problems can be computed by polynomial size nondeterministic circuits of unbounded fan-in with $O(\log\log n)$ depth and $O(\log^2 n)$ nondeterministic bits, ... 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 >>>


TR09-094 | 7th October 2009
Bireswar Das, Jacobo Toran, Fabian Wagner

Restricted Space Algorithms for Isomorphism on Bounded Treewidth Graphs

The Graph Isomorphism problem restricted to graphs of bounded treewidth or bounded tree distance width
are known to be solvable in polynomial time \cite{Bo90},\cite{YBFT}.
We give restricted space algorithms for these problems proving the following results:

Isomorphism for bounded tree distance width graphs is in L and thus complete ... 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 >>>




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