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Minimal pairs and complete problems
[chapter]

1990
*
Lecture Notes in Computer Science
*

Soare,

doi:10.1007/3-540-52282-4_29
fatcat:xojflc7fh5guvdatzfqdpzvmwe
*Minimal**pairs**and**complete**problems*, Theoretical Computer Science 132 (1994) 229-241. ...*And*there is a recursive oracle B relative to which Pf NP*and*the NP-*complete*sets are not the sup of a*minimal**pair*. ... Moreover, since F*and*G form a*minimal**pair*it follows that AF*and*A, form a*minimal**pair*too. ...##
###
Minimal pairs and complete problems

1994
*
Theoretical Computer Science
*

Soare,

doi:10.1016/0304-3975(94)90234-8
fatcat:bsnmcmwrnndcfbzdkwgl54cceq
*Minimal**pairs**and**complete**problems*, Theoretical Computer Science 132 (1994) 229-241. ...*And*there is a recursive oracle B relative to which Pf NP*and*the NP-*complete*sets are not the sup of a*minimal**pair*. ... Moreover, since F*and*G form a*minimal**pair*it follows that AF*and*A, form a*minimal**pair*too. ...##
###
TPL-Aware Displacement-driven Detailed Placement Refinement with Coloring Constraints

2015
*
Proceedings of the 2015 Symposium on International Symposium on Physical Design - ISPD '15
*

We prove that this

doi:10.1145/2717764.2717770
dblp:conf/ispd/LinC15
fatcat:bnuidur7ivflhf2u7foxclkjvi
*problem*is NP-*complete**and*show that it can be formulated as a mixed integer linear program. ... considering TPL coloring constraints for standard cells during detailed placement. • We prove that this new*problem*is NP-*complete*. • We propose a MILP formulation for this new*problem*. • Since MILP is ... METHODOLOGY Since the*problem*is NP-*complete**and*MILP is very time consuming, we propose an effective heuristic algorithm to solve this*problem*. ...##
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Page 316 of The Journal of the Operational Research Society Vol. 47, Issue 2
[page]

1996
*
The Journal of the Operational Research Society
*

Definition 1
For any

*pair*of jobs i, j from the same group, i > j if*and*only if p,/w; < p,/w;. ... We show that a schedule is feasible with respect to these precedence constraints if*and*only if it*minimizes*the total weighted*completion*time criterion. ...##
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Largest minimal inversion-complete and pair-complete sets of permutations
[article]

2015
*
arXiv
*
pre-print

The

arXiv:1503.00228v1
fatcat:bggqmwscizda7owvpwjxg2b2am
*problems*we consider are to determine the maximum cardinality of a*minimal*inversion-*complete*set of permutations,*and*that of a*minimal**pair*-*complete*set of permutations. ... It is*minimally*inversion-*complete*if in addition no proper subset of Q is inversion-*complete*;*and*similarly for*pair*-*completeness*. ... Therefore Q is*pair*-*complete*,*and*every*pair*(j, i) with i ≤ c < j is critical*and*covered by q j,i ∈ Q. Since |Q| = ⌊ n 2 4 ⌋ = |{(j, i) : 1 ≤ i ≤ c < j ≤ n}|, Q is*minimally**pair*-*complete*. ...##
###
Largest Minimal Inversion-Complete and Pair-Complete Sets of Permutations

2017
*
Combinatorica
*

The

doi:10.1007/s00493-016-3426-6
fatcat:rq6bitnmpfae7d7f6oavb22phm
*problems*we consider are to determine the maximum cardinality of a*minimal*inversioncomplete set of permutations,*and*that of a*minimal**pair*-*complete*set of permutations. ... It is*minimally*inversion-*complete*if in addition no proper subset of Q is inversion-*complete*;*and*similarly for*pair*-*completeness*. ... Therefore Q is*pair*-*complete*,*and*every*pair*(j, i) with i ≤ c < j is critical*and*covered by q j,i ∈ Q. Since |Q| = ⌊ n 2 4 ⌋ = |{(j, i) : 1 ≤ i ≤ c < j ≤ n}|, Q is*minimally**pair*-*complete*. ...##
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Hardness of Finding Two Edge-Disjoint Min-Min Paths in Digraphs
[chapter]

2011
*
Lecture Notes in Computer Science
*

The Min-Min

doi:10.1007/978-3-642-21204-8_32
fatcat:53ukdnvnwzghfngqrg5vbdlq6y
*problem*of finding a disjoint path*pair*with the length of the shorter path*minimized*is known to be NP-*complete**and*no K-approximation exists for any K ≥ 1 [1]. ... As a by-product, we show this*problem*remains NPcomplete even when all edge costs are equal (i.e. strongly NP-*complete*). ... (Min-Min*Problem*) Given an undirected (directed) graph G = (V, E), distinct vertices s, t ∈ V ,*and*a length function f : E → R + , find a vertex (edge) disjoint st-path*pair*AP*and*BP with f (AP )*minimized*...##
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Page 749 of The Journal of the Operational Research Society Vol. 59, Issue 6
[page]

2008
*
The Journal of the Operational Research Society
*

The

*problem*is to*minimize*the total distance travelled by 92 football league clubs over two*complete*fixtures. ... Instead, | try*and**minimize*the distance for two dates so that these fixtures can be used over the Christmas period. ...##
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The Dependency Pair Framework: Combining Techniques for Automated Termination Proofs
[chapter]

2005
*
Lecture Notes in Computer Science
*

To demonstrate this, we present several new techniques within the dependency

doi:10.1007/978-3-540-32275-7_21
fatcat:hcvrzqwszza7ljkvpdr4mat5ai
*pair*framework which simplify termination*problems*considerably. ... We implemented the dependency*pair*framework in our termination prover AProVE*and*evaluated it on large collections of examples. ... More precisely, a dependency*pair**problem*("DP*problem*", for short) consists of three TRSs P, Q,*and*R (where initially, P = DP (R))*and*a flag f ∈ {m, a} which stands for "*minimal*" or "arbitrary". ...##
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Page 1423 of Automation and Remote Control Vol. 27, Issue 8
[page]

1966
*
Automation and Remote Control
*

,

*and*the states of the corresponding*minimal*S-machine with*completely*regular PC -descrip- tion there exists a one-to-one correspondence. ... , corresponds to a*minimal*S-machine with a*completely*regular PC - description, Between the row headings of the*minimal*continuation table, i.e., between*pairs*pA, account being taken of their subscripts ...##
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Polynomial Time SAT Decision, Hypergraph Transversals and the Hermitian Rank
[chapter]

2005
*
Lecture Notes in Computer Science
*

Applications to heuristics for SAT algorithms

doi:10.1007/11527695_8
fatcat:lbc6dkmybjfhreu3xqbbf3wc7q
*and*to the structure of*minimally*unsatisfiable clause-sets are discussed. ... Combining graph theory*and*linear algebra, we study SAT*problems*of low "linear algebra complexity", considering formulas with bounded hermitian rank. ... challenges in hard combinatorial*problems**and*in optimization under 'uncertainty'". ...##
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Extremal minimality conditions on automata

2012
*
Theoretical Computer Science
*

In other words, we are interested on how the choice of the final states can affect the

doi:10.1016/j.tcs.2012.03.049
fatcat:5efof4lqgzhkbkwa3n6fwjmoiq
*minimality*of the automata. The state-*pair*graph is a useful tool to investigate such a*problem*. ... The choice of a set of final states for the automaton A defines a coloring of the closed components of the state-*pair*graph*and*the*minimality*of A corresponds to a property of these colored components ... of syntactic monoid*problem*makes it NP-*complete*. ...##
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Transitive closure, proximity and intransitivities

2003
*
Economic Theory
*

This result therefore provides a characterization of the transitive closure

doi:10.1007/s00199-003-0362-7
fatcat:7becj2w44vhujo5ck2mbadqa6y
*and*provides some degree of unification of two approaches to resolving the*problem*of intransitivities arising from Simple Majority ... It is then shown that the assignment of a weak order to a*complete*binary relation assigns its transitive closure if*and*only if it assigns the closest weak order according to a particular distance function ... Since this implies that g is not distance*minimizing*relative to d as assumed, there is a contradiction*and*this*completes*the proof. ...##
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Correlation Clustering – Minimizing Disagreements on Arbitrary Weighted Graphs
[chapter]

2003
*
Lecture Notes in Computer Science
*

We give an equivalence argument between these

doi:10.1007/978-3-540-39658-1_21
fatcat:byoheelyvrhq7lpbzc4aaholpm
*problems**and*the multicut*problem*. This implies an O(log n) approximation algorithm for*minimizing*disagreements on weighted*and*unweighted graphs. ... We solve several open*problems*concerning the correlation clustering*problem*introduced by Bansal, Blum*and*Chawla [1]. ... -Unweighted*Complete*Graphs Every*pair*of vertices has an edge between them,*and*every edge is labelled either + or − . ...##
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Complexity and Exact Algorithms for Multicut
[chapter]

2006
*
Lecture Notes in Computer Science
*

The Multicut

doi:10.1007/11611257_28
fatcat:7v6lkwv4arazfj7426mwme5q2y
*problem*is defined as: given an undirected graph*and*a collection of*pairs*of terminal vertices, find a minimum set of edges or vertices whose removal disconnects each*pair*. ... Complementing*and*refining previous results from the literature, we provide several NP-*completeness**and*(fixed-parameter) tractability results for restricted classes of graphs such as trees, interval graphs ... In most cases, the*problem*is NP-*complete*. There are many results*and*variants for Multicut*and*we refer to Costa, Létocart,*and*Roupin [2] for a recent survey. ...
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