Covering and packing in linear space
The fastest known algorithms for the k-cover and the k-packing problem rely on inclusion-exclusion and fast zeta transform, taking time and space 2(n), up to a factor polynomial in the size of the universe n. Here, we introduce a new, fast zeta transform algorithm that improves the space requirement to only linear in the size of the given set family, while not increasing the time requirement. Thus, for instance, the chromatic or domatic number of an n-vertex graph can be found in time within a polynomial factor of 2(n) and space O(1.442(n)) or O(1.716(n)), respectively. For computing the chromatic polynomial, we further reduce the space requirement to O(1.292(n)). (C) 2011 Elsevier B.V. All rights reserved.
algorithms zeta transform chromatic polynomial