WALCOM 2014: Algorithms and Computation pp 225-236

# Efficient Algorithms for Sorting k-Sets in Bins

• Atsuki Nagao
• Kazuhisa Seto
• Junichi Teruyama
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8344)

## Abstract

We give efficient algorithms for Sorting k-Sets in Bins. The Sorting k-Sets in Bins problem can be described as follows: We are given numbered n bins with k balls in each bin. Balls in the i-th bin are numbered n − i + 1. We can only swap balls between adjacent bins. How many swaps are needed to move all balls to the same numbered bins. For this problem, we design an efficient greedy algorithm with $$\frac{k+1}{4}n^2+O(kn)$$ swaps. As k and n increase, this approaches the lower bound of $$\lceil \binom{kn}{2}/(2k-1) \rceil$$. In addition, we design a more efficient recursive algorithm using $$\frac{15}{16}n^2+O(n)$$ swaps for the k = 3 case.

## Keywords

Greedy Mathematical puzzle Recursion Sorting Swap

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© Springer International Publishing Switzerland 2014

## Authors and Affiliations

• Atsuki Nagao
• 1
• Kazuhisa Seto
• 2
• Junichi Teruyama
• 3
• 4
1. 1.Kyoto UniversityJapan
2. 2.Seikei UniversityJapan
3. 3.National Institute of InformaticsJapan
4. 4.JST, ERATO, Kawarabayashi Large Graph Projectc/o Global Research Center for Big Data MathematicsJapan