Methods for task allocation via agent coalition formation

http://www.cs.cmu.edu/~sandholm/oralg.aij.pdf

Algorithm for optimal winner determination in combinatorial auctions

Routing and scheduling of vehicles and crews: The state of the art

In this paper we address ourselves to identifying facets of the set packing polyhedron, i.e., of the convex hull of integer solutions to the set covering problem with equality constraints and/or constraints of the form "ź". This is done by using the equivalent node-packing problem derived from the intersection graph associated with the problem under consideration. First, we show that the cliques of the intersection graph provide a first set of facets for the polyhedron in question. Second, it is shown that the cycles without chords of odd length of the intersection graph give rise to a further set of facets. A rather strong geometric property of this set of facets is exhibited.

On the facial structure of set packing polyhedra

Negotiation and cooperation in multi-agent environments

This paper gives an enumerative algorithm for the set-partitioning problem, that is, the set-covering problem with equality constraints, and presents computational results for real and randomly generated problems. The fact that many problems can be solved more rapidly than the corresponding linear programs demonstrates the efficiency of the algorithm; for example, a randomly generated problem with 1,400 variables and 100 constraints was solved in 15 minutes.

https://www.jstor.org/stable/pdfplus/168359.pdf

R. S. Garfinkel

Papers

The Set-Partitioning Problem: Set Covering with Equality Constraints