scholarly journals Fast RNC and NC algorithms for maximal path sets

1999 ◽  
Vol 215 (1-2) ◽  
pp. 89-98
Author(s):  
Ryuhei Uehara ◽  
Zhi-Zhong Chen ◽  
Xin He
Keyword(s):  
Maximal Path ◽  
Nc Algorithms

Parallel algorithms for matroid intersection and matroid parity

2015 ◽  
Vol 07 (02) ◽  
pp. 1550019
Author(s):  
Jinyu Huang
Keyword(s):  
Parallel Algorithms ◽  
Polynomial Identity ◽  
Black Box ◽  
Matroid Intersection ◽  
Polynomial Identity Testing ◽  
Identity Testing ◽  
Common Base ◽  
Graphic Matroid ◽  
Matroid Parity ◽  
Nc Algorithms

A maximum linear matroid parity set is called a basic matroid parity set, if its size is the rank of the matroid. We show that determining the existence of a common base (basic matroid parity set) for linear matroid intersection (linear matroid parity) is in NC2, provided that there are polynomial number of common bases (basic matroid parity sets). For graphic matroids, we show that finding a common base for matroid intersection is in NC2, if the number of common bases is polynomial bounded. To our knowledge, these algorithms are the first deterministic NC algorithms for matroid intersection and matroid parity. We also give a new RNC2 algorithm that finds a common base for graphic matroid intersection. We prove that if there is a black-box NC algorithm for Polynomial Identity Testing (PIT), then there is an NC algorithm to determine the existence of a common base (basic matroid parity set) for linear matroid intersection (linear matroid parity).

NC-ALGORITHMS FOR OPERATIONS ON BINARY DECISION DIAGRAMS

1993 ◽  
Vol 03 (01) ◽  
pp. 3-12 ◽  
Author(s):  
DETLEF SIELING ◽  
INGO WEGENER
Keyword(s):  
Binary Decision Diagrams ◽  
Pattern Generation ◽  
Decision Diagrams ◽  
Equivalence Test ◽  
Ordered Binary Decision Diagrams ◽  
Binary Decision ◽  
Verification Test ◽  
Logical Synthesis ◽  
Redundancy Test ◽  
Nc Algorithms

(Ordered) binary decision diagrams are a powerful representation for Boolean functions and are widely used in logical synthesis, verification, test pattern generation or as part of CAD tools. NC-algorithms are presented for the most important operations on this representation, e.g. evaluation for a given input, minimization, satisfiability, redundancy test, replacement of variables by constants or functions, equivalence test and synthesis. The algorithms have logarithmic run time on CRCW COMMON PRAMs with a polynomial number of processors.

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