Computationally Manageable Combinational Auctions
Management Science
Algorithmic mechanism design (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
Linear time algorithms for knapsack problems with bounded weights
Journal of Algorithms
Truth revelation in approximately efficient combinatorial auctions
Proceedings of the 1st ACM conference on Electronic commerce
Combinatorial auctions for supply chain formation
Proceedings of the 2nd ACM conference on Electronic commerce
Electronic Commerce Research
An efficient fully polynomial approximation scheme for the Subset-Sum problem
Journal of Computer and System Sciences
A Combinatorial Auction with Multiple Winners for Universal Service
Management Science
Approximately-strategyproof and tractable multiunit auctions
Decision Support Systems - Special issue: The fourth ACM conference on electronic commerce
Improved multi-unit auction clearing algorithms with interval (multiple-choice) knapsack problems
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
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We study the interval subset sum problem (ISSP), a generalization of the classic subset-sum problem, where given a set of intervals, the goal is to choose a set of integers, at most one from each interval, whose sum best approximates a target integer T. For the cardinality constrained interval subset-sum problem (kISSP), at least kmin and at most kmax integers must be selected. Our main result is a fully polynomial time approximation scheme for ISSP, with time and space both O(n . 1/ε). For kISSP, we present a 2-approximation with time O(n), and a FPTAS with time O( n . kmax . 1/ε ). Our work is motivated by auction clearing for uniform-price multi-unit auctions, which are increasingly used by security firms to allocate IPO shares, by governments to sell treasury bills, and by corporations to procure a large quantity of goods. These auctions use the uniform price rule – the bids are used to determine who wins, but all winning bidders receive the same price. For procurement auctions, a firm may even limit the number of winning suppliers to the range [kmin, kmax]. We reduce the auction clearing problem to ISSP, and use approximation schemes for ISSP to solve the original problem. The cardinality constrained auction clearing problem is reduced to kISSP and solved accordingly.