---
title: "The Multi-Inter-Distance Constraint"
authors:
  - "Pierre Ouellet"
  - "Claude-Guy Quimper"
doi: "10.5591/978-1-57735-516-8/IJCAI11-112"
url: "https://ijcai.org/proceedings/2011/112"
pdf: "https://ijcai.org/proceedings/2011/0112.pdf"
venue: "Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence"
year: 2011
pages: "629-633"
track: ""
keywords:
---

# The Multi-Inter-Distance Constraint

Pierre Ouellet, Claude-Guy Quimper

*Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence*, pages 629-633. DOI: [10.5591/978-1-57735-516-8/IJCAI11-112](https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-112)

## Abstract

We introduce the MULTI-INTER-DISTANCE constraint that ensures no more than m variables are assigned to values lying in a window of p consecutive values. This constraint is useful for modeling scheduling problems where tasks of processing time p compete for m identical resources. We present a propagator that achieves bounds consistency in cubic time. Experiments show that this new constraint offers a much stronger filtering than an edge-finder and that it allows to solve larger instances of the runway scheduling problem.