Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Tuesday, September 28, 2004, 12:15 pm

**Duration**: This information is not available in the database

**Location**: This information is not available in the database

**Speaker**: Michael Hoffmann

Given a simple undirected graph *G=(V,E)*, a positive integer *k*, and
three distinct vertices *s*, *t*, and *v* from *V*, is there a chordless path
from *s* via *v* to *t* in *G* that consists of at most *k* vertices? In a
chordless path, no two vertices are connected by an edge that is not
in the path. (Such paths are also known as induced paths.)

I will discuss the complexity of this problem that has been raised in
the context of service deployment in communication networks. In
particular, I will show that it is "unlikely" that this problem can be
solved in *f(k)*p(n)* time, for some arbitrary (e.g., doubly
exponential) function *f* and some polynomial *p*.

Similar results can be obtained for a number of related problems about
chordless paths, for example, for deciding on the existence of a
single directed chordless *(s,t)*-path in a digraph.

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