TY - GEN
T1 - On the approximability of combinatorial exchange problems
AU - Babaioff, Moshe
AU - Briest, Patrick
AU - Krysta, Piotr
PY - 2008
Y1 - 2008
N2 - In a combinatorial exchange the goal is to find a feasible trade between potential buyers and sellers requesting and offering bundles of indivisible goods. We investigate the approximability of several optimization objectives in this setting and show that the problems of surplus and trade volume maximization are inapproximable even with free disposal and even if each agent's bundle is of size at most 3. In light of the negative results for surplus maximization we consider the complementary goal of social cost minimization and present tight approximation results for this scenario. Considering the more general supply chain problem, in which each agent can be a seller and buyer simultaneously, we prove that social cost minimization remains inapproximable even with bundles of size 3, yet becomes polynomial time solvable for agents trading bundles of size 1 or 2. This yields a complete characterization of the approximability of supply chain and combinatorial exchange problems based on the size of traded bundles. We finally briefly address the problem of exchanges in strategic settings.
AB - In a combinatorial exchange the goal is to find a feasible trade between potential buyers and sellers requesting and offering bundles of indivisible goods. We investigate the approximability of several optimization objectives in this setting and show that the problems of surplus and trade volume maximization are inapproximable even with free disposal and even if each agent's bundle is of size at most 3. In light of the negative results for surplus maximization we consider the complementary goal of social cost minimization and present tight approximation results for this scenario. Considering the more general supply chain problem, in which each agent can be a seller and buyer simultaneously, we prove that social cost minimization remains inapproximable even with bundles of size 3, yet becomes polynomial time solvable for agents trading bundles of size 1 or 2. This yields a complete characterization of the approximability of supply chain and combinatorial exchange problems based on the size of traded bundles. We finally briefly address the problem of exchanges in strategic settings.
UR - http://www.scopus.com/inward/record.url?scp=44449178761&partnerID=8YFLogxK
U2 - 10.1007/978-3-540-79309-0_9
DO - 10.1007/978-3-540-79309-0_9
M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???
AN - SCOPUS:44449178761
SN - 3540793089
SN - 9783540793083
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 83
EP - 94
BT - Algorithmic Game Theory - First International Symposium, SAGT 2008, Proceedings
T2 - 1st International Symposium on Algorithmic Game Theory, SAGT 2008
Y2 - 30 April 2008 through 2 May 2008
ER -