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On Constrained Hypergraph Coloring and Nitin Ahuja and Anand Srivastav

Summary: On Constrained Hypergraph Coloring and
Nitin Ahuja and Anand Srivastav
Mathematisches Seminar
Christian-Albrechts-Universit¨at zu Kiel
Ludewig-Meyn-Str. 4, 24098 Kiel, Germany.
Abstract. We consider the design of approximation algorithms for mul-
ticolor generalization of the well known hypergraph 2-coloring problem
(property B). Consider a hypergraph H with n vertices, s edges, maxi-
mum edge degree D( s) and maximum vertex degree d( s). We study
the problem of coloring the vertices of H with minimum number of colors
such that no hyperedge i contains more than bi vertices of any color. The
main result of this paper is a deterministic polynomial time algorithm
for constructing approximate, (1 + )OPT -colorings ( (0, 1)) satis-
fying all constraints provided that bi's are logarithmically large in d and
two other parameters. This approximation ratio is independent of s. Our
lower bound on the bi's is better than the previous best bound. Due to
the similarity of structure these methods can also be applied to resource
constrained scheduling. We observe, using the non-approximability re-


Source: Ahuja, Nitin - Fachbereich Mathematik und Informatik, Technische Universität Braunschweig
Srivastav, Anand - Institut für Informatik, Christian-Albrechts-Universität Kiel


Collections: Computer Technologies and Information Sciences; Mathematics