Holographic algorithms
نویسندگان
چکیده
منابع مشابه
Holographic Algorithms
Leslie Valiant recently proposed a theory of holographic algorithms. These novel algorithms achieve exponential speed-ups for certain computational problems compared to naive algorithms for the same problems. The methodology uses Pfaffians and (planar) perfect matchings as basic computational primitives, and attempts to create exponential cancellations in computation. In this article we survey ...
متن کاملHolographic algorithms without matchgates
The theory of holographic algorithms, which are polynomial time algorithms for certain combinatorial counting problems, yields insight into the hierarchy of complexity classes. In particular, the theory produces algebraic tests for a problem to be in the class P. In this article we streamline the implementation of holographic algorithms by eliminating one of the steps in the construction proced...
متن کاملHolographic algorithms beyond matchgates
Holographic algorithms were first introduced by Valiant as a new methodology to derive polynomial time algorithms. The algorithms introduced by Valiant are based on matchgates, which are intrinsically for problems over planar structures. In this paper we introduce two new families of holographic algorithms. These algorithms work over general, i.e., not necessarily planar, graphs. Instead of mat...
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Article history: Available online xxxx Submitted by V. Mehrmann
متن کاملBases Collapse in Holographic Algorithms
Holographic algorithms are a novel approach to design polynomial time computations using linear superpositions. Most holographic algorithms are designed with basis vectors of dimension 2. Recently Valiant showed that a basis of dimension 4 can be used to solve in P an interesting (restrictive SAT) counting problem mod 7. This problem without modulo 7 is #P-complete, and counting mod 2 is NP-har...
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ژورنال
عنوان ژورنال: Current Developments in Mathematics
سال: 2005
ISSN: 1089-6384,2164-4829
DOI: 10.4310/cdm.2005.v2005.n1.a4