Efficient Algorithms for Envy-Free Stick Division With Fewest Cuts

Given a set of n sticks of various (not necessarily different) lengths, what is the largest length so that we can cut k equally long pieces of this length from the given set of sticks? We analyze the structure of this problem and show that it essentially reduces to a single call of a selection algorithm; we thus obtain an optimal linear-time algorithm. This algorithm also solves the related envy-free stick-division problem, which Segal-Halevi, Hassidim, and Aumann (AAMAS, 2015) recently used as their central primitive operation for the first discrete and bounded envy-free cake cutting protocol with a proportionality guarantee when pieces can be put to waste.Comment: v3 adds more context about the proble

A Practical and Worst-Case Efficient Algorithm for Divisor Methods of Apportionment

Proportional apportionment is the problem of assigning seats to parties according to their relative share of votes. Divisor methods are the de-facto standard solution, used in many countries. In recent literature, there are two algorithms that implement divisor methods: one by Cheng and Eppstein (ISAAC, 2014) has worst-case optimal running time but is complex, while the other (Pukelsheim, 2014) is relatively simple and fast in practice but does not offer worst-case guarantees. We demonstrate that the former algorithm is much slower than the other in practice and propose a novel algorithm that avoids the shortcomings of both. We investigate the running-time behavior of the three contenders in order to determine which is most useful in practice

Engineering Java 7's Dual Pivot Quicksort Using MaLiJAn

Wild S, Nebel M, Reitzig R, Laube U. Engineering Java 7's Dual Pivot Quicksort Using MaLiJan. In: Proceedings of the 15th Meeting on Algorithm Engineering and Experiments, ALENEX 2013, New Orleans, Louisiana, USA, January 7, 2013. Philadelphia, PA: Society for Industrial and Applied Mathematics; 2013: 55--69

JAGUC - A SOFTWARE PACKAGE FOR ENVIRONMENTAL DIVERSITY ANALYSES

Nebel M, Wild S, Holzhauser M, et al. Jaguc - a Software package for Environmental Diversity Analyses. J. Bioinformatics and Computational Biology. 2011;9(6):749--773