The Importance of Symmetric Representation

- A representation for a set is defined to be symmetric if the space required for the representation of the set is the same as the space required for representation of the set's complement. The use of symmetric representation is shown to be important when studying the time complexity of algorithms. In a study of the comparative complexity of NP-Complete problems in 1990, Stearns and Hunt presented an algorithm for CLIQUE with time complexity 2O e , where e is the number of edges in a graph. This result was interpreted to provide strong evidence that CLIQUE is an easier problem than INDEPENDENT SET, SATISFIABILITY and most other NP-Complete problems. Here we show that if the same algorithm is applied to a symmetric representation, it has time complexity 2 Or where r is the length of the representation. When symmetric representation is employed, there is no evidence that CLIQUE is easier than INDEPENDENT SET.

• Type: Journal
• Year: 2009
• Where: FCS
• Authors: Thomas O'Neil
• Keywords: Algorithm, Computer Science, FCS 2009, NP-complete Problems, Symmetric Representation