Convex Sequences and Combinatorial Counting

Vitaly A. Strusevich () and Kabir Rustogi
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Vitaly A. Strusevich: University of Greenwich
Kabir Rustogi: University of Greenwich

Chapter Chapter 5 in Scheduling with Time-Changing Effects and Rate-Modifying Activities, 2017, pp 91-102 from Springer

Abstract: Abstract In this chapter, we establish certain properties that are used on several occasions in this book. The main results that we present here primarily revolve around the convex and V-shaped finite sequences and the inequalities that govern them. We prove an inequality that involves an arbitrary non-decreasing function that depends on ceiling functions, thereby establishing the convexity and V-shapeness of the corresponding sequence. This sequence often appears in scheduling problems, especially when the jobs of a given set are to be divided into a known number of groups. The V-shapeness of this sequence enables us to speed up the running times of several algorithms that we consider in this book (see, e.g., Chaps. 16 and 17 ).

Date: 2017
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DOI: 10.1007/978-3-319-39574-6_5

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