Edge Finding Filtering Algorithm for Discrete Cumulative Resources in O(kn log n){\mathcal O}(kn {\rm log} n)

Petr Vilím

Abstract: This paper presents new Edge Finding algorithm for discrete cumulative resources, i.e. resources which can process several activities simultaneously up to some maximal capacity C. The algorithm has better time complexity than the current version of this algorithm: ${\mathcal O}(kn {\rm log} n)$ versus ${\mathcal O}(k n^2)$ where n is number of activities on the resource and k is number of distinct capacity demands. Moreover the new algorithm is slightly stronger and it is able to handle optional activities. The algorithm is based on the Θ-tree – a binary tree data structure which already proved to be very useful in filtering algorithms for unary resource constraints.