Covering and packing in linear space

Authors:
Andreas Björklund;Thore Husfeldt;Petteri Kaski;Mikko Koivisto
Affiliations:
Lund University, Department of Computer Science, P.O. Box 118, SE-22100 Lund, Sweden;Lund University, Department of Computer Science, P.O. Box 118, SE-22100 Lund, Sweden and IT University of Copenhagen, Rued Langgaards Vej 7, 2300, København S, Denmark;Helsinki Institute for Information Technology HIIT, Aalto University, Department of Information and Computer Science, P.O. Box 15400, FI-00076 Aalto, Finland;Helsinki Institute for Information Technology HIIT, University of Helsinki, Department of Computer Science, P.O. Box 68, FI-00014 University of Helsinki, Finland
Venue:
Information Processing Letters
Year:
2011

Citing 7
Cited 0

Fourier meets möbius: fast subset convolution

Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
On the Minimum Feedback Vertex Set Problem: Exact and Enumeration Algorithms

Algorithmica - Parameterized and Exact Algorithms
Combinatorial bounds via measure and conquer: Bounding minimal dominating sets and applications

ACM Transactions on Algorithms (TALG)
On Independent Sets and Bicliques in Graphs

Graph-Theoretic Concepts in Computer Science
Set Partitioning via Inclusion-Exclusion

SIAM Journal on Computing
Covering and packing in linear space

ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Fast exponential algorithms for maximum γ-regular induced subgraph problems

FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science

Quantified Score

Hi-index	0.90

Visualization

Abstract

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).