Review of recent development: The matroidal knapsack: A class of (often) well-solvable problems

Authors:
Paolo M. Camerini;Carlo Vercellis
Affiliations:
Centro di Studio per le Telecommunicazioni Spaziali of CNR, Milano, Italy;Dipartimento di Matematica, Università di Milano, Italy
Venue:
Operations Research Letters
Year:
1984

Citing 2
Cited 2

A computational study of a multiple-choice knapsack algorithm

ACM Transactions on Mathematical Software (TOMS)
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Matroidal relaxations for 0-1 knapsack problems

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Approximating multi-objective scheduling problems

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Abstract

A general class of problems, defined in terms of matroids, is recognized to include as special cases a variety of knapsack problems, subject to combinatorial constraints. A polynomial algorithm, based on Lagrangean relaxation, is proposed: A worst case and a probabilistic analysis demonstrate its ability to compute tight upper and lower bounds for the optimum, together with good approximate solutions.