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  1. SIAM Journal on Discrete Mathematics (SJDMEC)
  2. Volume 17
  3. Volume 17 Issue 1
  4. The Complexity of the Extendibility Problem for Finite Posets
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Volume 32
Volume 31
Volume 30
Volume 29
Volume 28
Volume 27
Volume 26
Volume 25
Volume 24
Volume 23
Volume 22
Volume 21
Volume 20
Volume 19
Volume 18
Volume 17
Volume 17 Issue 4
Volume 17 Issue 3
Volume 17 Issue 2
Volume 17 Issue 1
Acyclic Homomorphisms and Circular Colorings of Digraphs
Comparing Top k Lists
Cooperative Games under Augmenting Systems
The Complexity of the Extendibility Problem for Finite Posets
On Z2k -Linear and Quaternary Codes
Constrained Edge-Splitting Problems
Detachments Preserving Local Edge-Connectivity of Graphs
On the Homology of the h,k-Equal Dowling Lattice
Internet Routing and Related Topology Issues
Some New Aspects of the Coupon Collector's Problem
Volume 16
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Volume 14
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Volume 12
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Volume 10
Volume 9
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Volume 7
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Volume 5
Volume 4
Volume 3
Volume 2
Volume 1

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The Complexity of the Extendibility Problem for Finite Posets

Content Provider Society for Industrial and Applied Mathematics (SIAM)
Author Larose, Benoit Zdori, Lszl
Copyright Year 2003
Abstract For a finite poset P let EXT(P) denote the following decision problem. Given a finite poset Q and a partial map f from Q to P, decide whether f extends to a monotone total map from Q to P.It is easy to see that EXT(P) is in the complexity class NP. In [SIAM J. Comput., 28 (1998), pp. 57-104], Feder and Vardi define the classes of width 1 and of bounded strict width constraint satisfaction problems for finite relational structures. Both classes belong to the broader class of bounded width problems in P. We prove that for any finite poset P, if EXT(P) has bounded strict width, then it has width 1. In other words, if a poset admits a near unanimity operation, it also admits a totally symmetric idempotent operation of any arity. In [Fund. Inform., 28 (1996), pp. 165-182], Pratt and Tiuryn proved that SAT(P), a polynomial-time equivalent of EXT(P) is NP-complete if P is a crown. We generalize Pratt and Tiuryn's result on crowns by proving that EXT(P), is NP-complete for any finite poset P which admits no nontrivial idempotent Malcev condition.
Starting Page 114
Ending Page 121
Page Count 8
File Format PDF
ISSN 08954801
DOI 10.1137/S0895480101389478
e-ISSN 10957146
Journal SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number 1
Volume Number 17
Language English
Publisher Society for Industrial and Applied Mathematics
Publisher Date 2006-08-01
Access Restriction Subscribed
Subject Keyword zigzags Combinatorics of partially ordered sets totally symmetric idempotent and near unanimity operations extendibility problem for posets constraint satisfaction problem NP-complete Equational classes, universal algebra
Content Type Text
Resource Type Article
Subject Mathematics
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