All reports by Author Johannes Köbler:

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TR16-157
| 13th October 2016
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Vikraman Arvind, Johannes Köbler, Sebastian Kuhnert, Jacobo Toran#### Parameterized Complexity of Small Weight Automorphisms

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TR15-032
| 21st February 2015
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Vikraman Arvind, Johannes Köbler, Gaurav Rattan, Oleg Verbitsky#### Graph Isomorphism, Color Refinement, and Compactness

Revisions: 2

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TR14-096
| 29th July 2014
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Vikraman Arvind, Sebastian Kuhnert, Johannes Köbler, Jacobo Toran#### Solving Linear Equations Parameterized by Hamming Weight

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TR13-074
| 9th May 2013
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Johannes Köbler, Sebastian Kuhnert, Oleg Verbitsky#### Helly Circular-Arc Graph Isomorphism is in Logspace

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TR12-078
| 14th June 2012
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Vikraman Arvind, Sebastian Kuhnert, Johannes Köbler, Yadu Vasudev#### Approximate Graph Isomorphism

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TR12-032
| 4th April 2012
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Sebastian Kuhnert, Johannes Köbler, Osamu Watanabe#### Interval graph representation with given interval and intersection lengths

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TR10-043
| 5th March 2010
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Johannes Köbler, Sebastian Kuhnert, Bastian Laubner, Oleg Verbitsky#### Interval Graphs: Canonical Representation in Logspace

Revisions: 1

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TR09-093
| 8th October 2009
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Vikraman Arvind, Bireswar Das, Johannes Köbler, Seinosuke Toda#### Colored Hypergraph Isomorphism is Fixed Parameter Tractable

Revisions: 1

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TR09-092
| 8th October 2009
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Olaf Beyersdorff, Johannes Köbler, Sebastian Müller#### Proof Systems that Take Advice

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TR09-053
| 20th May 2009
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Johannes Köbler, Sebastian Kuhnert#### The Isomorphism Problem for k-Trees is Complete for Logspace

Revisions: 1

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TR08-075
| 7th July 2008
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Olaf Beyersdorff, Johannes Köbler, Sebastian Müller#### Nondeterministic Instance Complexity and Proof Systems with Advice

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TR98-037
| 29th June 1998
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Johannes Köbler, Rainer Schuler#### Average-Case Intractability vs. Worst-Case Intractability

Vikraman Arvind, Johannes Köbler, Sebastian Kuhnert, Jacobo Toran

We consider the PermCode problem to decide, given a representation of a permutation group G and a parameter k, whether there is a non-trivial element of G with support at most k. This problem generalizes several problems in the literature. We introduce a new method that allows to reduce the ... more >>>

Vikraman Arvind, Johannes Köbler, Gaurav Rattan, Oleg Verbitsky

Color refinement is a classical technique used to show that two given graphs $G$ and $H$

are non-isomorphic; it is very efficient, although it does not succeed on all graphs. We call a graph $G$ amenable to color refinement if the color-refinement procedure succeeds in distinguishing $G$ from any non-isomorphic ...
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Vikraman Arvind, Sebastian Kuhnert, Johannes Köbler, Jacobo Toran

Given a system of linear equations $Ax=b$ over the binary field $\mathbb{F}_2$ and an integer $t\ge 1$, we study the following three algorithmic problems:

1. Does $Ax=b$ have a solution of weight at most $t$?

2. Does $Ax=b$ have a solution of weight exactly $t$?

3. Does $Ax=b$ have a ...
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Johannes Köbler, Sebastian Kuhnert, Oleg Verbitsky

We present logspace algorithms for the canonical labeling problem and the representation problem of Helly circular-arc (HCA) graphs. The first step is a reduction to canonical labeling and representation of interval intersection matrices. In a second step, the Delta trees employed in McConnell's linear time representation algorithm for interval matrices ... more >>>

Vikraman Arvind, Sebastian Kuhnert, Johannes Köbler, Yadu Vasudev

We study optimization versions of Graph Isomorphism. Given two graphs $G_1,G_2$, we are interested in finding a bijection $\pi$ from $V(G_1)$ to $V(G_2)$ that maximizes the number of matches (edges mapped to edges or non-edges mapped to non-edges). We give an $n^{O(\log n)}$ time approximation scheme that for any constant ... more >>>

Sebastian Kuhnert, Johannes Köbler, Osamu Watanabe

We consider the problem of finding interval representations of graphs that additionally respect given interval lengths and/or pairwise intersection lengths, which are represented as weight functions on the vertices and edges, respectively. Pe'er and Shamir proved that the problem is NP-complete if only the former are given [SIAM J. Discr. ... more >>>

Johannes Köbler, Sebastian Kuhnert, Bastian Laubner, Oleg Verbitsky

We present a logspace algorithm for computing a canonical interval representation and a canonical labeling of interval graphs. As a consequence, the isomorphism and automorphism problems for interval graphs are solvable in logspace.

more >>>Vikraman Arvind, Bireswar Das, Johannes Köbler, Seinosuke Toda

We describe a fixed parameter tractable (fpt) algorithm for Colored Hypergraph Isomorphism} which has running time $b!2^{O(b)}N^{O(1)}$, where the parameter $b$ is the maximum size of the color classes of the given hypergraphs and $N$ is the input size. We also describe fpt algorithms for certain permutation group problems that ... more >>>

Olaf Beyersdorff, Johannes Köbler, Sebastian Müller

One of the starting points of propositional proof complexity is the seminal paper by Cook and Reckhow (JSL 79), where they defined

propositional proof systems as poly-time computable functions which have all propositional tautologies as their range. Motivated by provability consequences in bounded arithmetic, Cook and Krajicek (JSL 07) have ...
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Johannes Köbler, Sebastian Kuhnert

We show that k-tree isomorphism can be decided in logarithmic

space by giving a logspace canonical labeling algorithm. This improves

over the previous StUL upper bound and matches the lower bound. As a

consequence, the isomorphism, the automorphism, as well as the

canonization problem for k-trees ...
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Olaf Beyersdorff, Johannes Köbler, Sebastian Müller

Motivated by strong Karp-Lipton collapse results in bounded arithmetic, Cook and Krajicek have recently introduced the notion of propositional proof systems with advice.

In this paper we investigate the following question: Do there exist polynomially bounded proof systems with advice for arbitrary languages?

Depending on the complexity of the ...
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Johannes Köbler, Rainer Schuler

We use the assumption that all sets in NP (or other levels

of the polynomial-time hierarchy) have efficient average-case

algorithms to derive collapse consequences for MA, AM, and various

subclasses of P/poly. As a further consequence we show for

C in {P(PP), PSPACE} that ...
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