A Sublogarithmic Approximation for Tollbooth Pricing on Trees

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...

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Published inMathematics of operations research Vol. 42; no. 2; pp. 377 - 388
Main Authors Gamzu, Iftah, Segev, Danny
Format Journal Article
LanguageEnglish
Published Linthicum INFORMS 01.05.2017
Institute for Operations Research and the Management Sciences
Subjects
Algorithms
Approximation
approximation algorithms
balanced decompositions
Customers
Graph theory
highway problem
Mathematical analysis
Mathematical research
Methods
Operations research
Pricing
randomization
Revenue
segment guessing
Studies
tollbooth problem
Tolls
Trees
Trees (Graph theory)
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Abstract 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 (log m /log log m ), where m denotes the number of edges in the underlying graph. This finding improves on the currently best performance guarantees for trees, and up until recently, also on the best ratio for paths (commonly known as the highway problem). 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.
AbstractList 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(log m/log log m), where m denotes the number of edges in the underlying graph. This finding improves on the currently best performance guarantees for trees, and up until recently, also on the best ratio for paths (commonly known as the highway problem). 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.
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 (log m /log log m ), where m denotes the number of edges in the underlying graph. This finding improves on the currently best performance guarantees for trees, and up until recently, also on the best ratio for paths (commonly known as the highway problem). 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.
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(log m/log log m), where m denotes the number of edges in the underlying graph. This finding improves on the currently best performance guarantees for trees, and up until recently, also on the best ratio for paths (commonly known as the highway problem). 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.
Audience Academic
Author Segev, Danny
Gamzu, Iftah
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SubjectTerms Algorithms
Approximation
approximation algorithms
balanced decompositions
Customers
Graph theory
highway problem
Mathematical analysis
Mathematical research
Methods
Operations research
Pricing
randomization
Revenue
segment guessing
Studies
tollbooth problem
Tolls
Trees
Trees (Graph theory)
Title A Sublogarithmic Approximation for Tollbooth Pricing on Trees
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