TY - GEN

T1 - How to sell a graph

T2 - 32nd International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2006

AU - Grigoriev, Alexander

AU - Van Loon, Joyce

AU - Sitters, René

AU - Uetz, Marc

PY - 2006

Y1 - 2006

N2 - We consider a profit maximization problem where we are asked to price a set of m items that are to be assigned to a set of n customers. The items can be represented as the edges of an undirected (multi) graph G, where an edge multiplicity larger than one corresponds to multiple copies of the same item. Each customer is interested in purchasing a bundle of edges of G, and we assume that each bundle forms a simple path in G. Each customer has a known budget for her respective bundle, and is interested only in that particular bundle. The goal is to determine item prices and a feasible assignment of items to customers in order to maximize the total profit. When the underlying graph G is a path, we derive a fully polynomial time approximation scheme, complementing a recent NP-hardness result. If the underlying graph is a tree, and edge multiplicities are one, we show that the problem is polynomially solvable, contrasting its APX-hardness for the case of unlimited availability of items. However, if the underlying graph is a grid, and edge multiplicities are one, we show that it is even NP-complete to approximate the maximum profit to within a factor n 1-ε.

AB - We consider a profit maximization problem where we are asked to price a set of m items that are to be assigned to a set of n customers. The items can be represented as the edges of an undirected (multi) graph G, where an edge multiplicity larger than one corresponds to multiple copies of the same item. Each customer is interested in purchasing a bundle of edges of G, and we assume that each bundle forms a simple path in G. Each customer has a known budget for her respective bundle, and is interested only in that particular bundle. The goal is to determine item prices and a feasible assignment of items to customers in order to maximize the total profit. When the underlying graph G is a path, we derive a fully polynomial time approximation scheme, complementing a recent NP-hardness result. If the underlying graph is a tree, and edge multiplicities are one, we show that the problem is polynomially solvable, contrasting its APX-hardness for the case of unlimited availability of items. However, if the underlying graph is a grid, and edge multiplicities are one, we show that it is even NP-complete to approximate the maximum profit to within a factor n 1-ε.

KW - Computational complexity

KW - Dynamic programming

KW - Fully polynomial time approximation scheme

KW - Highway problem

KW - Pricing problems

KW - Tollbooth problem

UR - http://www.scopus.com/inward/record.url?scp=33845519057&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33845519057&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:33845519057

SN - 3540483810

SN - 9783540483816

VL - 4271 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 125

EP - 136

BT - Graph-Theoretic Concepts in Computer Science - 32nd International Workshop, WG 2006, Revised Papers

PB - Springer/Verlag

Y2 - 22 June 2006 through 24 June 2006

ER -