Years and Authors of Summarized Original Work
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2006, 2008; Valiant
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2008, 2009, 2010, 2011; Cai, Lu
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2009; Cai, Choudhary, Lu
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2014; Cai, Gorenstein
Problem Definition
Holographic algorithm, introduced by L. Valiant [11], is an algorithm design technique rather than a single algorithm for a particular problem. In essence, these algorithms are reductions to the FKT algorithm [7–9] to count the number of perfect matchings in a planar graph in polynomial time. Computation in these algorithms is expressed and interpreted through a choice of linear basis vectors in an exponential “holographic” mix, and then it is carried out by the FKT method via the Holant Theorem. This methodology has produced polynomial time algorithms for a variety of problems ranging from restrictive versions of satisfiability, vertex cover, to other graph problems such as edge orientation and node/edge deletion. No polynomial time algorithms were known for these problems, and some minor variations are known to be NP-hard...