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International Workshop on Combinatorial Algorithms

IWOCA 2014: Combinatorial Algorithms pp 250-261 | Cite as

Study of \(\kappa (D)\) for \(D = \{2, 3, x, y\}\)

  • Daniel Collister
  • Daphne Der-Fen Liu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8986)

Abstract

Let D be a set of positive integers. The kappa value of D, denoted by \(\kappa (D)\), is the parameter involved in the so called “lonely runner conjecture.” Let xy be positive integers, we investigate the kappa values for the family of sets \(D =\{2, 3, x, y\}\). For a fixed positive integer \(x > 3\), the exact values of \(\kappa (D)\) are determined for \(y=x+i\), \(1 \le i \le 6\). These results lead to some asymptotic behavior of \(\kappa (D)\) for \(D=\{2, 3, x, y\}\).

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.California State University Los AngelesLos AngelesUSA

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