A sublogarithmic approximation for highway and tollbooth pricing

Iftah Gamzu, Danny Segev

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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).

Original languageEnglish
Title of host publicationAutomata, Languages and Programming - 37th International Colloquium, ICALP 2010, Proceedings
Number of pages12
EditionPART 1
StatePublished - 2010
Event37th International Colloquium on Automata, Languages and Programming, ICALP 2010 - Bordeaux, France
Duration: 6 Jul 201010 Jul 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume6198 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference37th International Colloquium on Automata, Languages and Programming, ICALP 2010

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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