We develop a new algebraic technique that solves the following problem: Given
a black box that contains an arithmetic circuit f over a field of
characteristic 2 of degree d. Decide whether f, expressed as an
equivalent multivariate polynomial, contains a multilinear monomial of degree
This problem was solved by Williams W and Björklund et. al.
BHKK for a white box (the circuit is given as an input) that contains
arithmetic circuit. We show a simple black box algorithm that solves the
problem with the same time complexity.
This gives a simple randomized algorithm for the simple k-path problem for
directed graphs of the same time complexity[O^*(f(k)) is
O(poly(n)· f(k))] O^*(2^k) as in W and with reusing the same
ideas from BHKK with the above gives another algorithm (probably not
simpler) for undirected graphs of the same time complexity O^*(1.657^k) as in
Archived Files and Locations
|application/pdf 143.2 kB ||