TY - GEN

T1 - A sublogarithmic approximation for highway and tollbooth pricing

AU - Gamzu, Iftah

AU - Segev, Danny

PY - 2010

Y1 - 2010

N2 - An instance of the tollbooth problem consists of an undirected network and a collection of single-minded customers, each of which is interested in purchasing a fixed path subject to an individual budget constraint. The objective is to assign a per-unit price to each edge in a way that maximizes the collective revenue obtained from all customers. The revenue generated by any customer is equal to the overall price of the edges in her desired path, when this cost falls within her budget; otherwise, that customer will not purchase any edge. Our main result is a deterministic algorithm for the tollbooth problem on trees whose approximation ratio is O(logm / loglogm), where m denotes the number of edges in the underlying graph. This finding improves on the currently best performance guarantees for trees, due to Elbassioni et al. (SAGT '09), as well as for paths (commonly known as the highway problem), due to Balcan and Blum (EC '06). An additional interesting consequence is a computational separation between tollbooth pricing on trees and the original prototype problem of single-minded unlimited supply pricing, under a plausible hardness hypothesis due to Demaine et al. (SODA '06).

AB - An instance of the tollbooth problem consists of an undirected network and a collection of single-minded customers, each of which is interested in purchasing a fixed path subject to an individual budget constraint. The objective is to assign a per-unit price to each edge in a way that maximizes the collective revenue obtained from all customers. The revenue generated by any customer is equal to the overall price of the edges in her desired path, when this cost falls within her budget; otherwise, that customer will not purchase any edge. Our main result is a deterministic algorithm for the tollbooth problem on trees whose approximation ratio is O(logm / loglogm), where m denotes the number of edges in the underlying graph. This finding improves on the currently best performance guarantees for trees, due to Elbassioni et al. (SAGT '09), as well as for paths (commonly known as the highway problem), due to Balcan and Blum (EC '06). An additional interesting consequence is a computational separation between tollbooth pricing on trees and the original prototype problem of single-minded unlimited supply pricing, under a plausible hardness hypothesis due to Demaine et al. (SODA '06).

UR - http://www.scopus.com/inward/record.url?scp=77955339180&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-14165-2_49

DO - 10.1007/978-3-642-14165-2_49

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AN - SCOPUS:77955339180

SN - 3642141641

SN - 9783642141645

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

SP - 582

EP - 593

BT - Automata, Languages and Programming - 37th International Colloquium, ICALP 2010, Proceedings

T2 - 37th International Colloquium on Automata, Languages and Programming, ICALP 2010

Y2 - 6 July 2010 through 10 July 2010

ER -