Elsevier

Journal of Algorithms

Volume 11, Issue 1, March 1990, Pages 85-101
Journal of Algorithms

Sequence comparison with mixed convex and concave costs

https://doi.org/10.1016/0196-6774(90)90031-9Get rights and content

Abstract

Recently a number of algorithms have been developed for solving the minimum-weight edit sequence problem with non-linear costs for multiple insertions and deletions. We extend these algorithms to cost functions that are neither convex nor concave, but a mixture of both. We also apply this technique to related dynamic programming algorithms.

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    Indeed, let k⩾2 and assume that we already have computed all values F[j,k−1] with 1⩽j⩽n. For integers 0⩽j⩽i⩽n define the real-valued auxiliary function More general (and much more sophisticated) results on how to exploit Monge structures to speed up dynamic programming can be found in the work of Wilber [9], Eppstein [4], and Larmore and Schieber [6]. All the auxiliary values D[j], W[j], X[j], and Y[j] with 0⩽j⩽n can be computed in O(n) overall time.

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