Mathematical programming strategies for solving the minimum common string partition problem

Abstract

The minimum common string partition problem is an NP-hard combinatorial optimization problem with applications in computational biology. In this work we propose the first integer linear programming model for solving this problem. Moreover, on the basis of the integer linear programming model we develop a deterministic 2-phase heuristic which is applicable to larger problem instances. The results show that provenly optimal solutions can be obtained for problem instances of small and medium size from the literature by solving the proposed integer linear programming model with CPLEX. Furthermore, new best-known solutions are obtained for all considered problem instances from the literature. Concerning the heuristic, we were able to show that it outperforms heuristic competitors from the related literature.

Graph algorithms for DNA sequencing – origins, current models and the future

“…In this context one can also apply methods based on problems related to string similarity, such as e.g. some variant of the minimum common 425 string partition problem [44]. However, as heuristics, they cannot guarantee such a high precision as the alignment process.…”

An Integer Programming Formulation of the Minimum Common String Partition Problem

“…The first 10 (Group1) have lengths less than or equal to 200 bps (base-pairs), the next 10 (Group2) have lengths within [201, 400] and the rest 10 (Group3) have lengths within [401, 600] bps. Notably, these datases are also used for experimentation and analysis by researchers in recent papers [13, 14]. …”

“…We have also tested our formulation with a new random dataset collected through personal communication with Christian Blum, one of the co-authors of [14]. This new dataset is a collection of 300 uniform random instances of different lengths and alphabet sizes.…”

“…This dataset was introduced in [14] to test the solving limit of their ILP formulation. This constitutes 7 instances of length {800, 1000, 1200, 1400, 1600, 1800, 2000}.…”

“…The authors have tested their approach with the dataset introduced in [4]. Subsequently, a common block based ILP formulation has been proposed in [14] by Blum et al They have tested their ILP formulation on the previous benchmarks [4] as well as on a new benchmark of 7 larger instances.…”