scholarly journals ON THE COMPLEXITY OF SOME MALTSEV CONDITIONS

2009 ◽  
Vol 19 (01) ◽  
pp. 41-77 ◽  
Author(s):  
RALPH FREESE ◽  
MATTHEW A. VALERIOTE
Keyword(s):  
Polynomial Time ◽  
Finite Algebra ◽  
Free Algebras ◽  
Congruence Distributivity ◽  
Sharp Bounds ◽  
Polynomial Time Algorithms ◽  
Maltsev Conditions

This paper studies the complexity of determining if a finite algebra generates a variety that satisfies various Maltsev conditions, such as congruence distributivity or modularity. For idempotent algebras we show that there are polynomial time algorithms to test for these conditions but that in general these problems are EXPTIME complete. In addition, we provide sharp bounds in terms of the size of two-generated free algebras on the number of terms needed to witness various Maltsev conditions, such as congruence distributivity.

TERM EQUATION SATISFIABILITY OVER FINITE ALGEBRAS

2010 ◽  
Vol 20 (08) ◽  
pp. 1001-1020 ◽  
Author(s):  
TOMASZ A. GORAZD ◽  
JACEK KRZACZKOWSKI
Keyword(s):  
Computational Complexity ◽  
Polynomial Time ◽  
Finite Algebra ◽  
Satisfiability Problem ◽  
Finite Algebras ◽  
Maximal Clones ◽  
Polynomial Time Algorithms ◽  
Np Complete

We study the computational complexity of the satisfiability problem of an equation between terms over a finite algebra (TERM-SAT). We describe many classes of algebras where the complexity of TERM-SAT is determined by the clone of term operations. We classify the complexity for algebras generating maximal clones. Using this classification we describe many of algebras where TERM-SAT is NP-complete. We classify the situation for clones which are generated by an order or a permutation relation. We introduce the concept of semiaffine algebras and show polynomial-time algorithms which solve the satisfiability problem for them.

scholarly journals An Overview of Algorithms for Network Survivability

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
F. A. Kuipers
Keyword(s):  
Polynomial Time ◽  
Network Connectivity ◽  
Network Survivability ◽  
Disjoint Paths ◽  
Polynomial Time Algorithms ◽  
Concise Overview ◽  
Main Components

Network survivability—the ability to maintain operation when one or a few network components fail—is indispensable for present-day networks. In this paper, we characterize three main components in establishing network survivability for an existing network, namely, (1) determining network connectivity, (2) augmenting the network, and (3) finding disjoint paths. We present a concise overview of network survivability algorithms, where we focus on presenting a few polynomial-time algorithms that could be implemented by practitioners and give references to more involved algorithms.

scholarly journals Reconstruction of score sets

2014 ◽  
Vol 6 (2) ◽  
pp. 210-229
Author(s):  
Antal Iványi
Keyword(s):  
Polynomial Time ◽  
Constructive Proof ◽  
Construction Algorithm ◽  
Polynomial Time Algorithms ◽  
General Polynomial ◽  
Degree Set ◽  
New Algorithms

Abstract The score set of a tournament is defined as the set of its different outdegrees. In 1978 Reid [15] published the conjecture that for any set of nonnegative integers D there exists a tournament T whose degree set is D. Reid proved the conjecture for tournaments containing n = 1, 2, and 3 vertices. In 1986 Hager [4] published a constructive proof of the conjecture for n = 4 and 5 vertices. In 1989 Yao [18] presented an arithmetical proof of the conjecture, but general polynomial construction algorithm is not known. In [6] we described polynomial time algorithms which reconstruct the score sets containing only elements less than 7. In [5] we improved this bound to 9. In this paper we present and analyze new algorithms Hole-Map, Hole-Pairs, Hole-Max, Hole-Shift, Fill-All, Prefix-Deletion, and using them improve the above bound to 12, giving a constructive partial proof of Reid’s conjecture.

scholarly journals Polynomial-Time Algorithms for Stochastic Uncapacitated Lot-Sizing Problems

2008 ◽  
Vol 56 (5) ◽  
pp. 1172-1183 ◽  
Author(s):  
Yongpei Guan ◽  
Andrew J. Miller
Keyword(s):  
Polynomial Time ◽  
Lot Sizing ◽  
Polynomial Time Algorithms
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