Some optimal inapproximability results
Journal of the ACM (JACM)
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
On profit-maximizing envy-free pricing
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Noise stability of functions with low in.uences invariance and optimality
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Combination can be hard: approximability of the unique coverage problem
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Single-minded unlimited supply pricing on sparse instances
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Approximation algorithms and online mechanisms for item pricing
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Optimal Inapproximability Results for MAX-CUT and Other 2-Variable CSPs?
SIAM Journal on Computing
On Hardness of Pricing Items for Single-Minded Bidders
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Conditional Hardness for Approximate Coloring
SIAM Journal on Computing
On Profit-Maximizing Pricing for the Highway and Tollbooth Problems
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
On the Complexity of the Highway Pricing Problem
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
Two-query PCP with subconstant error
Journal of the ACM (JACM)
A theory of loss-leaders: making money by pricing below cost
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
A sublogarithmic approximation for highway and tollbooth pricing
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Hardness of Max-2Lin and Max-3Lin over Integers, Reals, and Large Cyclic Groups
CCC '11 Proceedings of the 2011 IEEE 26th Annual Conference on Computational Complexity
How to sell a graph: guidelines for graph retailers
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Near-optimal pricing in near-linear time
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
On the complexity of the highway problem
Theoretical Computer Science
A path-decomposition theorem with applications to pricing and covering on trees
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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Consider the problem of pricing n items under an unlimited supply with m buyers. Each buyer is interested in a bundle of at most k of the items. These buyers are single minded, which means each of them has a budget and they will either buy all the items if the total price is within their budget or they will buy none of the items. The goal is to price each item with profit margin p1, p2,..., pn so as to maximize the overall profit. When k = 2, such a problem is called the graph-vertex-pricing problem. Another special case of the problem is the highway-pricing problem when the items (toll-booths) are arranged linearly on a line and each buyer (as a driver) is interested in paying for a path that consists of consecutive items. The goal again is to price the items (tolls) so as to maximize the total profits. There is an O(k)-approximation algorithm by [BB06] when the price on each item must be above its margin cost; i.e., pi 0 for every i ε [n]. As for the highway problem, a PTAS is shown in [GR11]. We investigate the above problem when the seller is allowed to price some of the items below their margin cost. It is shown in [BB06, BBCH07] that by pricing some of the items below cost, the maximum profit can increase by a factor of Ω(log n). These items sold at low prices to stimulate other profitable sales are called "loss leaders". Given the possibility of making more profit, understanding the approximability of pricing loss leaders for graph-vertex-pricing, highway-pricing as well as the general item pricing problem are formulated as open problems in [BB06,BBCH07]. In this paper, we obtain strong hardness of approximation result for the problem of pricing loss leaders. First we show that it is NP-hard to get better than O(log log log n)-approximation when k ≥ 3. This improves a previous super-constant hardness result assuming the Unique Games Conjecture [Wu11]. In addition, we show a super-constant Unique-Games hardness for the highway-pricing problem as well as the graph-vertex-pricing problem.