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Convex Sequences and Combinatorial Counting

In: Scheduling with Time-Changing Effects and Rate-Modifying Activities

Author

Listed:
  • Vitaly A. Strusevich

    (University of Greenwich)

  • Kabir Rustogi

    (University of Greenwich
    Delhivery Logistics Pvt. Ltd.)

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 ).

Suggested Citation

  • Vitaly A. Strusevich & Kabir Rustogi, 2017. "Convex Sequences and Combinatorial Counting," International Series in Operations Research & Management Science, in: Scheduling with Time-Changing Effects and Rate-Modifying Activities, chapter 0, pages 91-102, Springer.
    • Handle: RePEc:spr:isochp:978-3-319-39574-6_5
    DOI: 10.1007/978-3-319-39574-6_5
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