Dividing splittable goods evenly and with limited fragmentation
Paper i proceeding, 2017

A splittable good provided in n pieces shall be divided as evenly as possible among m agents, where every agent can take shares of at most F pieces. We call F the fragmentation. For F=1 we can solve the max-min and min-max problems in linear time. The case F=2 has neat formulations and structural characterizations in terms of weighted graphs. Here we focus on perfectly balanced solutions. While the problem is strongly NP-hard in general, it can be solved in linear time if m>n-2, and a solution always exists in this case. Moreover, case F=2 is fixed-parameter tractable in the parameter 2m-n. The results also give rise to various open problems.

load balancing

linear-time algorithm

weighted graph

packing

parameterized algorithm

Författare

Peter Damaschke

Chalmers, Data- och informationsteknik, Datavetenskap

Leibniz International Proceedings in Informatics, LIPIcs

18688969 (ISSN)

Vol. 83 9:1 - 9:13

Ämneskategorier

Beräkningsmatematik

Diskret matematik

Fundament

Grundläggande vetenskaper

DOI

10.4230/LIPIcs.MFCS.2017.9

ISBN

978-395977046-0