Exact algorithm and heuristic for the Closest String Problem

Improved LP-based algorithms for the closest string problem

“…As for ECPA, a time limit of 30 s has been applied to the ILP solver for the larger instances when tackling the ILP model. We do not provide results for the McClure instances [5] as algorithm RA already reaches the optimum for all instances in at most 0.11 s (notice that the optimum of instance ''Mc586.6.seq'' is 72 while in [4] is erroneously indicated 70). Also, we do not provide the results of A and B as they were dominated by BCPA not only in terms of quality (as shown above) but also in terms of CPU time.…”

“…We tested these algorithms on the same instances tackled in [4] kindly provided by the authors and compared the results to those of algorithm LDDA_LSS presented in [4]. The tests were performed on a Pentium IV Quad Core CPU at 2.66 GHz with 3.5 GB of RAM.…”

“…Finally, Algorithm C of [1] provides some diversification with respect to B by applying B starting from eight different initial configurations related to the first variable rounded up. Here, RA is an instant algorithm that derives its solution directly from the optimal solution of the continuous relaxation of model (1)- (5) and is correspondingly much faster than A, B or C. BCPA first solves to optimality the continuous relaxation of model (1)-(5) and then a very small size (at least for all the instances considered in [4]) ILP model. Notice that it can be easily shown that BCPA dominates both A and B.…”

“…. n and constraints (3) indicate that for each string s i , the Hamming distance between t and s i must not exceed d. Finally, constraints (4) indicate that all x(j,k) variables are binary, while constraint (5) indicates that d is positive.…”

“…All these papers indicate that by exploiting a suitable ILP formulation of the problem high-quality heuristic approaches can be obtained. In a recent paper on this journal [4], a polynomial time heuristic procedure called LDDA_LSS is proposed for CSP. Notice that in all these papers and in many others available in the literature only instances with n b m are considered.…”