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Electronic Colloquium on Computational Complexity

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All reports by Author Georg Schnitger:

TR15-127 | 7th August 2015
Stasys Jukna, Georg Schnitger

On the Optimality of Bellman--Ford--Moore Shortest Path Algorithm

Revisions: 1

We prove a general lower bound on the size of branching programs over any semiring of zero characteristic, including the (min,+) semiring. Using it, we show that the classical dynamic programming algorithm of Bellman, Ford and Moore for the shortest s-t path problem is optimal, if only Min and Sum ... more >>>

TR09-008 | 15th January 2009
Stasys Jukna, Georg Schnitger

Min-Rank Conjecture for Log-Depth Circuits

A completion of an m-by-n matrix A with entries in {0,1,*} is obtained
by setting all *-entries to constants 0 or 1. A system of semi-linear
equations over GF(2) has the form Mx=f(x), where M is a completion of
A and f:{0,1}^n --> {0,1}^m is an operator, the i-th coordinate ... more >>>

TR01-066 | 28th September 2001
Pavol Duris, Juraj Hromkovic, Stasys Jukna, Martin Sauerhoff, Georg Schnitger

On Multipartition Communication Complexity

We study k-partition communication protocols, an extension
of the standard two-party best-partition model to k input partitions.
The main results are as follows.

1. A strong explicit hierarchy on the degree of
non-obliviousness is established by proving that,
using k+1 partitions instead of k may decrease
the communication complexity from ... more >>>

TR01-049 | 11th July 2001
Stasys Jukna, Georg Schnitger

On Multi-Partition Communication Complexity of Triangle-Freeness

Comments: 2

We show that recognizing the $K_3$-freeness and $K_4$-freeness of
graphs is hard, respectively, for two-player nondeterministic
communication protocols with exponentially many partitions and for
nondeterministic (syntactic) read-$s$ times branching programs.

The key ingradient is a generalization of a coloring lemma, due to
Papadimitriou and Sipser, which says that for every ... more >>>

TR00-076 | 24th August 2000
Juraj Hromkovic, Juhani Karhumaki, Hartmut Klauck, Georg Schnitger, Sebastian Seibert

Measures of Nondeterminism in Finite Automata

While deterministic finite automata seem to be well understood, surprisingly
many important problems
concerning nondeterministic finite automata (nfa's) remain open.

One such problem area is the study of different measures of nondeterminism in
finite automata and the
estimation of the sizes of minimal nondeterministic finite automata. In this
paper the ... more >>>

TR99-007 | 10th March 1999
Juraj Hromkovic, Georg Schnitger

On the Power of Las Vegas II: Two-Way Finite Automata

The investigation of the computational power of randomized
computations is one of the central tasks of current complexity and
algorithm theory. This paper continues in the comparison of the computational
power of LasVegas computations with the computational power of deterministic
and nondeterministic ones. While for one-way ... more >>>

TR97-029 | 20th August 1997
Pavol Duris, Juraj Hromkovic, Jose' D. P. Rolim, Georg Schnitger

On the Power of Las Vegas for One-way Communication Complexity, Finite Automata, and Polynomial-time Computations

The study of the computational power of randomized
computations is one of the central tasks of complexity theory. The
main goal of this paper is the comparison of the power of Las Vegas
computation and deterministic respectively nondeterministic
computation. We investigate the power of Las Vegas computation for ... more >>>

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