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Minimal pairs and complete problems [chapter]

Klaus Ambos-Spies, Steven Homer, Robert I. Soare
1990 Lecture Notes in Computer Science  
Soare, 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.  ... 
doi:10.1007/3-540-52282-4_29 fatcat:xojflc7fh5guvdatzfqdpzvmwe

Minimal pairs and complete problems

Klaus Ambos-Spies, Steven Homer, Robert I. Soare
1994 Theoretical Computer Science  
Soare, 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.  ... 
doi:10.1016/0304-3975(94)90234-8 fatcat:bsnmcmwrnndcfbzdkwgl54cceq

TPL-Aware Displacement-driven Detailed Placement Refinement with Coloring Constraints

Tao Lin, Chris Chu
2015 Proceedings of the 2015 Symposium on International Symposium on Physical Design - ISPD '15  
We prove that this 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.  ... 
doi:10.1145/2717764.2717770 dblp:conf/ispd/LinC15 fatcat:bnuidur7ivflhf2u7foxclkjvi

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.  ... 

Largest minimal inversion-complete and pair-complete sets of permutations [article]

Eric Balandraud, Maurice Queyranne, Fabio Tardella
2015 arXiv   pre-print
The 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.  ... 
arXiv:1503.00228v1 fatcat:bggqmwscizda7owvpwjxg2b2am

Largest Minimal Inversion-Complete and Pair-Complete Sets of Permutations

Eric Balandraud, Fabio Tardella, Maurice Queyranne
2017 Combinatorica  
The 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.  ... 
doi:10.1007/s00493-016-3426-6 fatcat:rq6bitnmpfae7d7f6oavb22phm

Hardness of Finding Two Edge-Disjoint Min-Min Paths in Digraphs [chapter]

Longkun Guo, Hong Shen
2011 Lecture Notes in Computer Science  
The Min-Min 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  ... 
doi:10.1007/978-3-642-21204-8_32 fatcat:53ukdnvnwzghfngqrg5vbdlq6y

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.  ... 

The Dependency Pair Framework: Combining Techniques for Automated Termination Proofs [chapter]

Jürgen Giesl, René Thiemann, Peter Schneider-Kamp
2005 Lecture Notes in Computer Science  
To demonstrate this, we present several new techniques within the dependency 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".  ... 
doi:10.1007/978-3-540-32275-7_21 fatcat:hcvrzqwszza7ljkvpdr4mat5ai

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  ... 

Polynomial Time SAT Decision, Hypergraph Transversals and the Hermitian Rank [chapter]

Nicola Galesi, Oliver Kullmann
2005 Lecture Notes in Computer Science  
Applications to heuristics for SAT algorithms 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'".  ... 
doi:10.1007/11527695_8 fatcat:lbc6dkmybjfhreu3xqbbf3wc7q

Extremal minimality conditions on automata

Antonio Restivo, Roberto Vaglica
2012 Theoretical Computer Science  
In other words, we are interested on how the choice of the final states can affect the 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.  ... 
doi:10.1016/j.tcs.2012.03.049 fatcat:5efof4lqgzhkbkwa3n6fwjmoiq

Transitive closure, proximity and intransitivities

Nick Baigent, Christian Klamler
2003 Economic Theory  
This result therefore provides a characterization of the transitive closure 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.  ... 
doi:10.1007/s00199-003-0362-7 fatcat:7becj2w44vhujo5ck2mbadqa6y

Correlation Clustering – Minimizing Disagreements on Arbitrary Weighted Graphs [chapter]

Dotan Emanuel, Amos Fiat
2003 Lecture Notes in Computer Science  
We give an equivalence argument between these 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 − .  ... 
doi:10.1007/978-3-540-39658-1_21 fatcat:byoheelyvrhq7lpbzc4aaholpm

Complexity and Exact Algorithms for Multicut [chapter]

Jiong Guo, Falk Hüffner, Erhan Kenar, Rolf Niedermeier, Johannes Uhlmann
2006 Lecture Notes in Computer Science  
The Multicut 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.  ... 
doi:10.1007/11611257_28 fatcat:7v6lkwv4arazfj7426mwme5q2y
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