Fair allocation of indivisible goods under conflict constraints release_lshrz3meevhxjmac6hex2daqg4

by Nina Chiarelli, Matjaž Krnc, Martin Milanič, Ulrich Pferschy, Nevena Pivač, Joachim Schauer

Released as a article .

2021  

Abstract

We consider the fair allocation of indivisible items to several agents and add a graph theoretical perspective to this classical problem. Thereby we introduce an incompatibility relation between pairs of items described in terms of a conflict graph. Every subset of items assigned to one agent has to form an independent set in this graph. Thus, the allocation of items to the agents corresponds to a partial coloring of the conflict graph. Every agent has its own profit valuation for every item. Aiming at a fair allocation, our goal is the maximization of the lowest total profit of items allocated to any one of the agents. The resulting optimization problem contains, as special cases, both Partition and Independent Set. In our contribution we derive complexity and algorithmic results depending on the properties of the given graph. We can show that the problem is strongly NP-hard for bipartite graphs and their line graphs, and solvable in pseudo-polynomial time for the classes of chordal graphs, cocomparability graphs, biconvex bipartite graphs, and graphs of bounded treewidth. Each of the pseudo-polynomial algorithms can also be turned into a fully polynomial approximation scheme (FPTAS).
In text/plain format

Archived Content

There are no accessible files associated with this release. You could check other releases for this work for an accessible version.

"Dark" Preservation Only
Save Paper Now!

Know of a fulltext copy of on the public web? Submit a URL and we will archive it

Type  article
Stage   submitted
Date   2021-01-12
Version   v2
Language   en ?
arXiv  2003.11313v2
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: ff7cc532-318f-4041-811b-8201f71c9afe
API URL: JSON