Distance-Constrained Elementary Path Problem : Comparison of MIP Formulations Sebastien François 1 , Rumen Andonov 1 Univ Rennes, Inria, CNRS, IRISA, Rennes, France, sefra35@gmail.com, randonov@irisa.fr Mots-clés : Graphs, Optimization, Longest Path Problem 1 Introduction Here we analyse various MIP formulations for the so called Distance-Constrained Elementary Path (DCEP) problem. It can be formulated as follows : given a directed graph G =(V,E,l) where l e ≥ 0 denotes the weight associated with each arc e ∈ E. In addition, it is given a set DC of vertex pairs (called distance constraints ) such that any couple (u, v) ∈ DC is associated with a distance interval [d (u, v), d(u, v)]. We say that a path  P in G satisfies the distance constraint dc(u, v)=[d (u, v), d(u, v)] if both u and v are on  P and the subpath of  P between u and v has length in dc(u, v). The goal is to find an elementary path in G that maximizes the number of satisfied distance constraints. DCEP has been introduced in one of our previous papers where two MIP formulations have been also given [6]. Here we continue the analysis and the comparison of these formulations and report extensive numerical results. 2 DCEP motivation and similarity with famous problems DCEP is motivated by the genome assembly problem which is a challenging computational task in bioinformatics aiming at reconstructing the full genome of an organism from short DNA sequences (reads ) [7]. No satisfactory solution for DCEP is known today and heuristics are essentially described in the literature [9, 1, 2]. The methodology that we propose in [4, 5] differs significantly from these heuristics since it is based on integer programming model for solving genome assembly as a problem of finding a long simple path in a specific graph, which satisfies additional constraints encoding the insert-size (distance) information. We thus develop a global optimization approach where the various assembly steps are simultaneously solved in the framework of a common objective function. The numerical experiments show that our tool produces assemblies of significantly higher quality than some widely-used heuristics on a chloroplast genomes benchmark. These results fully justify the efforts for designing exact approaches for genome assembly. 3 Similarity with famous problems While the paper [5] is application oriented, in [6] we revisit the mixed integer linear program- ming formulation proposed there from a combinatorial optimization viewpoint. Furthermore, we show how to adapt the well known Miller, Tucker and Zemlin (MTZ) formulation for solving the longest path problem [8] in order to solve the DCEP problem. Note that the challenges in DCEP problem are somehow similar, but harder in practice, to the ones in solving lon- gest/shortest (with real weights) elementary path problems [3, 10]. For example one of the hardest constraints in the MIP formulation for DCEP is the sub-tour elimination contraint.