Abstract
We describe here a technique applicable to integer programming problems which we refer to as IP2. An IP2 problem has linear constraints where each constraint has up to three variables with nonzero coefficients, and one of the three variables appear in that constraint only. The technique is used to identify either polynomial time solvability of the problem in time that is required to solve a minimum cut problem on an associated graph; or in case the problem is NP-hard the technique is used to generate superoptimal solution all components of which are integer multiple of \( \tfrac{1} {2} \) In some of the latter cases, for minimization problems, the half integral solution may be rounded to a feasible solution that is provably within a factor of 2 of the optimum.
Research supported in part by NSF award No. DMI-9713482, NSF award No. DMI- 9908705.
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Hochbaum, D.S. (2000). Instant Recognition of Polynomial Time Solvability, Half Integrality, and 2-Approximations. In: Jansen, K., Khuller, S. (eds) Approximation Algorithms for Combinatorial Optimization. APPROX 2000. Lecture Notes in Computer Science, vol 1913. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44436-X_2
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DOI: https://doi.org/10.1007/3-540-44436-X_2
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