TY - GEN
T1 - A knapsack secretary problem with applications
AU - Babaioff, Moshe
AU - Immorlica, Nicole
AU - Kempe, David
AU - Kleinberg, Robert
PY - 2007
Y1 - 2007
N2 - We consider situations in which a decision-maker with a fixed budget faces a sequence of options, each with a cost and a value, and must select a subset of them online so as to maximize the total value. Such situations arise in many contexts, e.g., hiring workers, scheduling jobs, and bidding in sponsored search auctions. This problem, often called the online knapsack problem, is known to be inapproximable. Therefore, wo make the enabling assumption that elements arrive in a random order. Hence our problem can be thought of as a weighted version of the classical secretary problem, which we call the knapsack secretary problem. Using the random-order assumption, we design a constant-competitive algorithm for arbitrary weights and values, as well as a e-competitive algorithm for the special case when all weights are equal (i.e., the multiple-choice secretary problem). In contrast to previous work on online knapsack problems, we do not assume any knowledge regarding the distribution of weights and values beyond the fact that the order is random.
AB - We consider situations in which a decision-maker with a fixed budget faces a sequence of options, each with a cost and a value, and must select a subset of them online so as to maximize the total value. Such situations arise in many contexts, e.g., hiring workers, scheduling jobs, and bidding in sponsored search auctions. This problem, often called the online knapsack problem, is known to be inapproximable. Therefore, wo make the enabling assumption that elements arrive in a random order. Hence our problem can be thought of as a weighted version of the classical secretary problem, which we call the knapsack secretary problem. Using the random-order assumption, we design a constant-competitive algorithm for arbitrary weights and values, as well as a e-competitive algorithm for the special case when all weights are equal (i.e., the multiple-choice secretary problem). In contrast to previous work on online knapsack problems, we do not assume any knowledge regarding the distribution of weights and values beyond the fact that the order is random.
UR - http://www.scopus.com/inward/record.url?scp=38049039420&partnerID=8YFLogxK
U2 - 10.1007/978-3-540-74208-1_2
DO - 10.1007/978-3-540-74208-1_2
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AN - SCOPUS:38049039420
SN - 9783540742074
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 16
EP - 28
BT - Approximation, Randomization, and Combinatorial Optimization
PB - Springer Verlag
T2 - 10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and 11th International Workshop on Randomization and Computation, RANDOM 2007
Y2 - 20 August 2007 through 22 August 2007
ER -