Finding Nearest Larger Neighbors

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Abstract

Designing and analysing efficient algorithms is important in practical applications, but it is also fun and frequently instructive, even for simple problems with no immediate applications. In this self-contained paper we try to convey some of fun of algorithm design and analysis. Hopefully, the reader will find the discussion instructive as well.

We focus our attention on a single problem that we call the All Nearest Larger Neighbors Problem. Part of the fun in designing algorithms for this problem is the rich variety of algorithms that arise under slightly different optimization criteria. We also illustrate several important analytic techniques, including amortization, and correctness arguments using non-trivial loop invariants.

We hope, in this modest way, to reflect our deep admiration for the many contributions of Kurt Mehlhorn to the theory, practice and appreciation of algorithm design and analysis.