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Inclusion-exclusion...
Inclusion-exclusion algorithms for counting set partitions
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- Björklund, Andreas (författare)
- Lund University,Lunds universitet,Institutionen för datavetenskap,Institutioner vid LTH,Lunds Tekniska Högskola,Department of Computer Science,Departments at LTH,Faculty of Engineering, LTH
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- Husfeldt, Thore (författare)
- Lund University,Lunds universitet,Data Vetenskap,Naturvetenskapliga fakulteten,Institutionen för datavetenskap,Institutioner vid LTH,Lunds Tekniska Högskola,Computer Science,Faculty of Science,Department of Computer Science,Departments at LTH,Faculty of Engineering, LTH
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(creator_code:org_t)
- 2006
- 2006
- Engelska 8 s.
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Ingår i: 2006 47th Annual IEEE Conference on Foundations of Computer Science. - 0769527205 ; , s. 575-582
- Relaterad länk:
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http://dx.doi.org/10...
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https://lup.lub.lu.s...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- Given a set U with n elements and a family of subsets S ⊆ 2U we show how to count the number of k-partitions S1 ∪ ... ∪ Sk = U into subsets Si ∈ S in time 2nnO(1). The only assumption on S is that it can be enumerated in time 2nnO(1). In effect we get exact algorithms in time 2nnO(1) for several well-studied partition problems including domatic number, chromatic number, bounded component spanning forest, partition into Hamiltonian subgraphs, and bin packing. If only polynomial space is available, our algorithms run in time 3nnO(1) if membership in S can be decided in polynomial time. For chromatic number, we present a version that runs in time O(2.2461n) and polynomial space. For domatic number, we present a version that runs in time O(2.8718n). Finally, we present a family of polynomial space approximation algorithms that find a number between χ(G) and [(1 + ϵ)χ(G)] in time O(1.2209n + 2.2461e-ϵn)
Ämnesord
- NATURVETENSKAP -- Data- och informationsvetenskap -- Datavetenskap (hsv//swe)
- NATURAL SCIENCES -- Computer and Information Sciences -- Computer Sciences (hsv//eng)
Nyckelord
- polynomial space approximation
- bin packing
- Hamiltonian subgraph
- bounded component spanning forest
- chromatic number
- domatic number
- inclusion-exclusion algorithm
- counting set partition
Publikations- och innehållstyp
- kon (ämneskategori)
- ref (ämneskategori)
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