Bundle Pricing with Comparable Items

Grigoriev, Alexander; Loon, Joyce van; Sviridenko, Maxim; Uetz, Marc; Vredeveld, Tjark

doi:10.1007/978-3-540-75520-3_43

Cited by 11 publications

(17 citation statements)

References 10 publications

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“…Moreover, Balcan and Blum [3] derive an O(k)-approximation algorithm, given that each customer is interested in a subset of at most k items. Under the additional restriction that a larger bundle is more expensive than a smaller one, Grigoriev et al [12] present a PTAS.…”

Section: Related Workmentioning

confidence: 98%

“…Guruswami et al [13] furthermore propose a polynomial time dynamic programming algorithm when the budgets are bounded by a constant, and a pseudopolynomial time dynamic programming algorithm when the number of edges in the customers' paths is bounded by a constant. For the highway problem with additional constraint that a longer path should be more expensive than a shorter path, there exists a log B-approximation algorithm [12], where B is the largest budget. For the highway problem in which customers have a nonunit demand and edge capacities are limited, Elbassioni et al [8] present a quasi-polynomial time approximation scheme.…”

Section: Related Workmentioning

confidence: 99%

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Optimal pricing of capacitated networks

Grigoriev¹,

Loon²,

Sitters

et al. 2008

Networks

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We address the algorithmic complexity of a profit maximization problem in capacitated, undirected networks. We are asked to price a set of m capacitated network links to serve a set of n potential customers. Each customer is interested in purchasing a network connection that is specified by a simple path in the network and has a maximum budget that we assume to be known to the seller. The goal is to decide which customers to serve, and to determine prices for all network links in order to maximize the total profit. We address this pricing problem in different network topologies. More specifically, we derive several results on the algorithmic complexity of this profit maximization problem, given that the network is either a path, a cycle, a tree, or a grid. Our results include approximation algorithms as well as inapproximability results.

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Section: Related Workmentioning

confidence: 98%

Section: Related Workmentioning

confidence: 99%

Optimal pricing of capacitated networks

Grigoriev¹,

Loon²,

Sitters

et al. 2008

Networks

Self Cite

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“…Therefore, it is beyond the scope of this writing to do justice and present an exhaustive survey of previous work. We refer the reader to directly related papers [19,16,1,5,8,9,21,6,10,22] and to the references therein for a more comprehensive review of the literature.…”

Section: Related Workmentioning

confidence: 99%

A Sublogarithmic Approximation for Highway and Tollbooth Pricing

Gamzu

Segev

2010

Automata, Languages and Programming

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An instance of the tollbooth problem consists of an undirected network and a collection of singleminded 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, 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).An extensively-studied question in economics and operations management is that of pricing an assortment of products in a given market, trying to maximize revenue subject to a multitude of constraints. Somewhat informally, the inherent difficulty in such settings boils down to the obvious tension between two extremes: low prices attract more customers, while high prices generate greater revenues per purchase. Recently, the spotlights have been turned on computational challenges in pricing. What seems to be the driving force behind this line of research is an immense growth in the range of sources for acquiring costumer preferences data, which are now available as a result of the widespread use of the Internet.The tollbooth problem. One particular computational task that has received much recent attention is the tollbooth problem, which captures optimization-related aspects of pricing connection links in networks, e.g., setting prices for road use in a system of toll highways. Formally, an instance of this problem consists of an undirected graph G = (V, E) with m edges, which can be broadly interpreted as products with unlimited supply. An additional ingredient of the input is a collection C of n single-minded customers, each of which is interested in purchasing a fixed path subject to an individual budget constraint. Technically speaking, the demand attributes of customer i are represented by a pair (P i , b i ), where P i ⊆ G is the path she wishes to buy, and b i stands for her budget, namely, the maximum price she is willing to pay for that path. Any customer will buy a single unit of each edge in the desired path when its total cost falls within her budget; otherwise, she leaves without buying anything. With this setting in mind, the goal is to assign a per-unit price to each edge in a way that maximizes the overall revenue. More precisely...

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“…Balcan and Blum [1] derive an O(log m)-approximation algorithm for the highway problem, improving upon the previous O(log m + log n)-approximation of Guruswami et al [8], where m is the number of highway segments and n is the number of customers. Under the monotonicity condition that the total price of any given path is no more than the total price of a longer path, Grigoriev et al [7] show that a O(log B)-approximation exists, where B is an upper bound on the valuations. Furthermore, Grigoriev et al [6] derive an FPTAS, assuming that the maximum capacity of any segment of the highway is bounded by a constant.…”

Section: Related Workmentioning

confidence: 99%

On the Complexity of the Highway Pricing Problem

Grigoriev

Loon

Uetz

2010

SOFSEM 2010: Theory and Practice of Computer Science

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On the Complexity of the Highway Pricing Problem RM/08/030 JEL code: C44, C61 Abstract. The highway pricing problem asks for prices to be determined for segments of a single highway such as to maximize the revenue obtainable from a given set of customers with known valuations. The problem is (weakly) NP-hard and a recent quasi-PTAS suggests that a PTAS might be in reach. Yet, so far it has resisted any attempt for constant-factor approximation algorithms. We relate the tractability of the problem to structural properties of customers' valuations. We show that the problem becomes NP-hard as soon as the average valuations of customers are not homogeneous, even under further restrictions such as monotonicity. Moreover, we derive an efficient approximation algorithm, parameterized along the inhomogeneity of customers' valuations. Finally, we discuss extensions of our results that go beyond the highway pricing problem.

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Bundle Pricing with Comparable Items

Cited by 11 publications

References 10 publications

Optimal pricing of capacitated networks

Optimal pricing of capacitated networks

A Sublogarithmic Approximation for Highway and Tollbooth Pricing

On the Complexity of the Highway Pricing Problem

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