LP Based Parameterized Algorithms
Years and Authors of Summarized Original Work
2013; Cygan, Pilipczuk, Pilipczuk, Wojtaszczyk
2014; Lokshtanov, Narayanaswamy, Raman, Ramanujan, Saurabh
Linear and integer programs have played a crucial role in the theory of approximation algorithms for combinatorial optimization problems. While they have also been central in identifying polynomial time solvable problems, it is only recently that these tools have been put to use in designing exact algorithms for NP-complete problems. Following the paradigm of above-guarantee parameterization in fixed-parameter tractability, these efforts have focused on designing algorithms where the exponential component of the running time depends only on the excess of the solution above the optimum value of a linear program for the problem.
The linear program obtained from a given integer linear program (ILP) by relaxing the integrality conditions on the variables is called the standard relaxation...
KeywordsAbove guarantee parameterizations FPT algorithms Linear programming
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