The.Algorithm.Design.Manual.Springer-Verlag.1998

Knapsack Problem
Pascal implementations of several knapsack algorithms, including backtracking and a refined greedy
algorithm, are provided in [SDK83]. See Section for details.
Notes: Martello and Toth's book [MT90a] and survey article [MT87] are the standard references on the
knapsack problem, including most theoretical and experimental results. An excellent exposition on
integer programming approaches to knapsack problems appears in [SDK83]. See [FP75a] for a
computational study of algorithms for 0-1 knapsack problems.
A polynomial-time approximation scheme is an algorithm that approximates the optimal solution of a
problem in time polynomial in both its size and the approximation factor . This very strong condition
implies a smooth tradeoff between running time and approximation quality. Good expositions on the
polynomial-time approximation scheme [IK75] for knapsack and subset sum includes [Baa88, CLR90,
GJ79, Man89].
The first algorithm for generalized public key encryption by Merkle and Hellman [MH78] was based on
the hardness of the knapsack problem. See [Sch94] for an exposition.
Related Problems: Bin packing (see page ), integer programming (see page ).
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Algorithms
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