Years and Authors of Summarized Original Work
2013; Cygan, Pilipczuk, Pilipczuk, Wojtaszczyk
2014; Lokshtanov, Narayanaswamy, Raman, Ramanujan, Saurabh
2014; Wahlstrom
Problem Definition
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.
Method Description
The linear program obtained from a given integer linear program (ILP) by relaxing the integrality conditions on the variables is called the standard relaxation...
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Chitnis RH, Cygan M, Hajiaghayi M, Pilipczuk M, Pilipczuk M (2012) Designing FPT algorithms for cut problems using randomized contractions. In: 53rd annual IEEE symposium on foundations of computer science, FOCS 2012, New Brunswick, 20–23 Oct 2012, pp 460–469
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Cygan M, Pilipczuk M, Pilipczuk M, Wojtaszczyk JO (2013) On multiway cut parameterized above lower bounds. Trans Comput Theory 5(1):3
Guillemot S (2011) FPT algorithms for path-transversal and cycle-transversal problems. Discret Optim 8(1):61–71
Hochbaum DS (2002) Solving integer programs over monotone inequalities in three variables: a framework for half integrality and good approximations. Eur J Oper Res 140(2):291–321
Iwata Y, Oka K, Yoshida Y (2014) Linear-time FPT algorithms via network flow. In: Proceedings of the twenty-fifth annual ACM-SIAM symposium on discrete algorithms, SODA 2014, Portland, 5–7 Jan 2014, pp 1749–1761
Lokshtanov D, Narayanaswamy NS, Raman V, Ramanujan MS, Saurabh S (2014) Faster parameterized algorithms using linear programming. ACM Trans Algorithms 11(2):15
Narayanaswamy NS, Raman V, Ramanujan MS, Saurabh S (2012) LP can be a cure for parameterized problems. In: 29th international symposium on theoretical aspects of computer science, STACS 2012, Paris, 29th Feb – 3rd Mar 2012, pp 338–349
Nemhauser GL, Trotter LE (1974) Properties of vertex packing and independence system polyhedra. Math Program 6:48–61
Nemhauser GL, Trotter LE (1975) Vertex packings: structural properties and algorithms. Math Program 8:232–248
Reed BA, Smith K, Vetta A (2004) Finding odd cycle transversals. Oper Res Lett 32(4):299–301
Wahlström M (2014) Half-integrality, LP-branching and FPT algorithms. In: Proceedings of the twenty-fifth annual ACM-SIAM symposium on discrete algorithms, SODA 2014, Portland, 5–7 Jan 2014, pp 1762–1781
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Ramanujan, M.S. (2016). LP Based Parameterized Algorithms. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_778
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