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1.
The constrained two-dimensional cutting (C_TDC) problem consists of determining a cutting pattern of a set of n small rectangular piece types on a rectangular stock plate of length L and width W, as to maximize the sum of the profits of the pieces to be cut. Each piece type i, i = 1, …, n, is characterized by a length li, a width wi, a profit (or weight) ci and an upper demand value bi. The upper demand value is the maximum number of pieces of type i which can be cut on rectangle ( L, W). In this paper, we study the two-staged fixed orientation C_TDC, noted FC_2TDC. It is a classical variant of the C_TDC where each piece is produced, in the final cutting pattern, by at most two guillotine cuts, and each piece has a fixed orientation. We solve the FC_2TDC problem using several approximate algorithms, that are mainly based upon a strip generation procedure. We evaluate the performance of these algorithms on instances extracted from the literature. 相似文献
2.
, for the monotone depth of functions in monotone-P. As a result we achieve the separation of the following classes.
1. monotone-NC ≠ monotone-P.
2. For every i≥1, monotone-≠ monotone-.
3. More generally: For any integer function D( n), up to (for some ε>0), we give an explicit example of a monotone Boolean function, that can be computed by polynomial size monotone
Boolean circuits of depth D( n), but that cannot be computed by any (fan-in 2) monotone Boolean circuits of depth less than Const· D( n) (for some constant Const).
Only a separation of monotone- from monotone- was previously known.
Our argument is more general: we define a new class of communication complexity search problems, referred to below as DART
games, and we prove a tight lower bound for the communication complexity of every member of this class. As a result we get
lower bounds for the monotone depth of many functions. In particular, we get the following bounds:
1. For st-connectivity, we get a tight lower bound of . That is, we get a new proof for Karchmer–Wigderson's theorem, as an immediate corollary of our general result.
2. For the k-clique function, with , we get a tight lower bound of Ω( k log n). This lower bound was previously known for k≤ log n [1]. For larger k, however, only a bound of Ω( k) was previously known.
Received: December 19, 1997 相似文献
3.
We introduce a Gentzen-style sequent calculus axiomatization for Basic Predicate Calculus. Our new axiomatization is an improvement
of the previous axiomatizations, in the sense that it has the subformula property. In this system the cut rule is eliminated.
Received: 18 April 2000 / Published online: 2 September 2002
Mathematics Subject Classification (2000): Primary 03F05; Secondary 03F99, 03B60
Key words or phrases: Basic predicate calculus – Cut elimination – Sequent 相似文献
4.
We study a general multiobjective optimization problem with variational inequality, equality, inequality and abstract constraints.
Fritz John type necessary optimality conditions involving Mordukhovich coderivatives are derived. They lead to Kuhn-Tucker
type necessary optimality conditions under additional constraint qualifications including the calmness condition, the error
bound constraint qualification, the no nonzero abnormal multiplier constraint qualification, the generalized Mangasarian-Fromovitz
constraint qualification, the strong regularity constraint qualification and the linear constraint qualification. We then
apply these results to the multiobjective optimization problem with complementarity constraints and the multiobjective bilevel
programming problem.
Received: November 2000 / Accepted: October 2001 Published online: December 19, 2002
Key Words. Multiobjective optimization – Variational inequality – Complementarity constraint – Constraint qualification – Bilevel programming
problem – Preference – Utility function – Subdifferential calculus – Variational principle
Research of this paper was supported by NSERC and a University of Victoria Internal Research Grant
Research was supported by the National Science Foundation under grants DMS-9704203 and DMS-0102496
Mathematics Subject Classification (2000): Sub49K24, 90C29 相似文献
5.
We consider diffusions corresponding to the generator
for continuous with γ
i
nonnegative. We show uniqueness for the corresponding martingale problem under certain non-degeneracy conditions on b
i
, γ
i
and present a counter-example when these conditions are not satisfied. As a special case, we establish uniqueness in law
for some classes of super-Markov chains with state dependent branching rates and spatial motions.
Received: 31 March 2001 / Revised version: 6 November 2001 / Published online: 1 July 2002 相似文献
6.
We introduce a new upper bound for the maximum-entropy sampling problem. Our bound is described as the solution of a linear
integer program. The bound depends on a partition of the underlying set of random variables. For the case in which each block
of the partition has bounded cardinality, we describe an efficient dynamic-programming algorithm to calculate the bound. For
the very special case in which the blocks have no more than two elements, we describe an efficient algorithm for calculating
the bound based on maximum-weight matching. This latter formulation has particular value for local-search procedures that
seek to find a good partition. We relate our bound to recent bounds of Hoffman, Lee and Williams. Finally, we report on the
results of some computational experiments.
Received: September 27, 2000 / Accepted: July 26, 2001 Published online: September 5, 2002
Key words. experimental design – design of experiments – entropy – maximum-entropy sampling – matching – integer program – spectral
bound – Fischer's inequality – branch-and-bound – dynamic programming
Mathematics Subject Classification (2000): 52B12, 90C10
Send offprint requests to: Jon Lee
Correspondence to: Jon Lee 相似文献
7.
Let be an increasing nonconstant sequence of positive real numbers. Under certain conditions on this sequence we prove the following
inequality
where n, m ∈ ℕ and r is a positive number, a
n
! denotes . The upper bound is the best possible. This inequality generalizes the Martins’ inequality. A special case of the above inequality
solves an open problem by F. Qi in Generalization of H. Alzer’s Inequality, J. Math. Anal. Appl. 240 (1999), 294–297.
Received September 18, 2001; in revised form August 14, 2002 相似文献
8.
We study a special case of a structured mixed integer programming model that arises in production planning. For the most
general case of the model, called PI, we have earlier identified families of facet–defining valid inequalities: ( l, S) inequalities (introduced for the uncapacitated lot–sizing problem by Barany, Van Roy, and Wolsey), cover inequalities, and
reverse cover inequalities. PI is 𝒩𝒫–hard; in this paper we focus on a special case, called PIC. We describe a polynomial
algorithm for PIC, and we use this algorithm to derive an extended formulation of polynomial size for PIC. Projecting from
this extended formulation onto the original space of variables, we show that ( l, S) inequalities, cover inequalities, and reverse cover inequalities suffice to solve the special case PIC by linear programming.
We also describe fast combinatorial separation algorithms for cover and reverse cover inequalities for PIC. Finally, we discuss
the relationship between our results for PIC and a model studied previously by Goemans.
Received: December 13, 2000 / Accepted: December 13, 2001 Published online: October 9, 2002
RID="★"
ID="★" Some of the results in this paper have appeared in condensed form in Miller et al. (2001).
Key words. mixed integer programming – polyhedral combinatorics – production planning – capacitated lot–sizing – fixed charge network
flow – setup times
This paper presents research results of the Belgian Program on Interuniversity Poles of Attraction initiated by the Belgian
State, Prime Minister's Office, Science Policy Programming. The scientific responsibility is assumed by the authors.
This research was also supported by NSF Grant No. DMI-9700285 and by Philips Electronics North America. 相似文献
9.
Let S
ni be a star of size n
i and let S= S
n1∪…∪ S
nk≠ S
2n−3∪ S
1 or S
2∪ S
2 be a spanning star-forest of the complete graph K
2n. We prove that K
2n has a proper (2 n−1)-edge-colouring such that all the edges of S receive distinct colours. This result is very useful in the study of total-colourings of graphs.
Received: March 8, 1995 / Revised: May 16, 1997 相似文献
10.
In terms of formal deductive systems and multi-dimensional Kripke frames we study logical operations know, informed, common knowledge and common information. Based on [6] we introduce formal axiomatic systems for common information logics and prove that these systems are sound
and complete. Analyzing the common information operation we show that it can be understood as greatest open fixed points for
knowledge formulas. Using obtained results we explore monotonicity, omniscience problem, and inward monotonocity, describe
their connections and give dividing examples. Also we find algorithms recognizing these properties for some particular cases.
Received: 21 October 2000 / Published online: 2 September 2002
Key words or phrases: Multi-agent systems – Non-standard logic – Knowledge representation – Common knowledge – Common information – Fixed points,
Kripke models – Modal logic 相似文献
11.
In this paper we consider the problem of bounding the Betti numbers, b
i
( S), of a semi-algebraic set S⊂ℝ
k
defined by polynomial inequalities P
1≥0,…, P
s
≥0, where P
i
∈ℝ[ X
1,…, X
k
], s< k, and deg ( P
i
)≤2, for 1≤ i≤ s. We prove that for 0≤ i≤ k−1, This improves the bound of k
O(s) proved by Barvinok (in Math. Z. 225:231–244, 1997). This improvement is made possible by a new approach, whereby we first bound the Betti numbers of non-singular complete
intersections of complex projective varieties defined by generic quadratic forms, and use this bound to obtain bounds in the
real semi-algebraic case.
The first author was supported in part by an NSF grant CCF-0634907. The second author was partially supported by NSF grant
CCF-0634907 and the European RTNetwork Real Algebraic and Analytic Geometry, Contract No. HPRN-CT-2001-00271. 相似文献
12.
The split cuts of Cook, Kannan and Schrijver are general-purpose valid inequalities for integer programming which include a variety of other
well-known cuts as special cases. To detect violated split cuts, one has to solve the associated separation problem. The complexity of split cut separation was recently cited as an open problem by Cornuéjols & Li CL01.
In this paper we settle this question by proving strong 𝒩𝒫-completeness of separation for split cuts. As a by-product we
also show 𝒩𝒫-completeness of separation for several other classes of inequalities, including the MIR-inequalities of Nemhauser and Wolsey and some new inequalities which we call balanced split cuts and binary split cuts. We also strengthen 𝒩𝒫-completeness results of Caprara & Fischetti CF96 (for
-cuts) and Eisenbrand E99 (for Chvátal-Gomory cuts).
To compensate for this bleak picture, we also give a positive result for the Symmetric Travelling Salesman Problem. We show how to separate in polynomial time over a class of split cuts which includes all comb inequalities with a fixed handle.
Received: October 23, 2000 / Accepted: October 03, 2001 Published online: September 5, 2002
Key words. cutting planes – separation – complexity – travelling salesman problem – comb inequalities 相似文献
13.
This paper presents a cut-elimination procedure for classical and intuitionistic logic, in which cut is eliminated directly,
without introducing the mix rule. The well-known problem of cut eliminations, when in the derivation the contractions of the
cut-formulae are above the premisses of the cut, will be solved by new transformations of the derivation.
Received: 1 June 2001 /
Published online: 5 November 2002
Mathematics Subject Classification (2000): 03F05
Key words or phrases: Systems of sequents – Cut-elimination theorem 相似文献
14.
Let S={ s i } i∈??? be a numerical semigroup. For s i ∈ S, let ν( s i ) denote the number of pairs ( s i ? s j , s j )∈ S 2. When S is the Weierstrass semigroup of a family $\{\mathcal{C}_{i}\}_{i\in\mathbb{N}}Let S={s
i
}
i∈ℕ⊆ℕ be a numerical semigroup. For s
i
∈S, let ν(s
i
) denote the number of pairs (s
i
−s
j
,s
j
)∈S
2. When S is the Weierstrass semigroup of a family
{Ci}i ? \mathbbN\{\mathcal{C}_{i}\}_{i\in\mathbb{N}} of one-point algebraic-geometric codes, a good bound for the minimum distance of the code Ci\mathcal{C}_{i} is the Feng and Rao order bound
d
ORD
(C
i
). It is well-known that there exists an integer m such that d
ORD
(C
i
)=ν(s
i+1) for each i≥m. By way of some suitable parameters related to the semigroup S, we find upper bounds for m and we evaluate m exactly in many cases. Further we conjecture a lower bound for m and we prove it in several classes of semigroups. 相似文献
15.
The standard quadratic program (QPS) is
min xεΔx TQx, where
is the simplex Δ = {x ⩽ 0 ∣ ∑ i=1n x i = 1}. QPS can be used to formulate combinatorial problems such as the maximum stable set problem, and also arises in global
optimization algorithms for general quadratic programming when the search space is partitioned using simplices. One class
of ‘d.c.’ (for ‘difference between convex’) bounds for QPS is based on writing Q= S− T, where S and T are both positive semidefinite, and bounding
x T Sx (convex on Δ) and −x Tx
(concave on Δ) separately. We show that the maximum possible such bound can be obtained by solving a semidefinite programming
(SDP) problem. The dual of this SDP problem corresponds to adding a simple constraint to the well-known Shor relaxation of
QPS. We show that the max d.c. bound is dominated by another known bound based on a copositive relaxation of QPS, also obtainable
via SDP at comparable computational expense. We also discuss extensions of the d.c. bound to more general quadratic programming
problems. For the application of QPS to bounding the stability number of a graph, we use a novel formulation of the Lovasz
ϑ number to compare ϑ, Schrijver’s ϑ′, and the max d.c. bound. 相似文献
16.
In this paper, we present a nonlinear programming algorithm for solving semidefinite programs (SDPs) in standard form. The
algorithm's distinguishing feature is a change of variables that replaces the symmetric, positive semidefinite variable X of the SDP with a rectangular variable R according to the factorization X= RR
T
. The rank of the factorization, i.e., the number of columns of R, is chosen minimally so as to enhance computational speed while maintaining equivalence with the SDP. Fundamental results
concerning the convergence of the algorithm are derived, and encouraging computational results on some large-scale test problems
are also presented.
Received: March 22, 2001 / Accepted: August 30, 2002 Published online: December 9, 2002
Key Words. semidefinite programming – low-rank factorization – nonlinear programming – augmented Lagrangian – limited memory BFGS
This research was supported in part by the National Science Foundation under grants CCR-9902010, INT-9910084, CCR-0203426
and CCR-0203113 相似文献
17.
The k-partitioning problem is defined as follows: Given a set of items { I
1, I
2,..., I
n} where item Ij is of weight wj 0, find a partition S
1, S
2,..., S
m
of this set with ¦ S
i
¦ = k such that the maximum weight of all subsets S
i
is minimal, k-partitioning is strongly related to the classical multiprocessor scheduling problem of minimizing the makespan on identical machines. This paper provides suitable tools for the construction of algorithms which solve exactly the problem. Several approximation algorithms are presented for this NP-hard problem. The worst-case behavior of the algorithms is analyzed. The best of these algorithms achieves a performance bound of 4/3. 相似文献
18.
Let S be a bounded region in R
N and let ℊ={ S
i}
i
=1/m
be a partition of S into a finite number of subsets having piecewise C
2 boundaries. We assume that where C
2 segments of the boundaries meet, the angle subtended by tangents to these segments at the point of contact is bounded away
from 0. Let τ: S → S be piecewise C
2 on ℊ and expanding in the sense that there exists 0< σ< 1 such that for any i=1, 2, ..., m, ‖ Dτ
i
−1
‖< σ, where Dτ
i
−1
is the derivative matrix of τ
i
−1
and ‖ ‖ is the euclidean matrix norm. The main result provides an upper bound on σ which guarantees the existence of an absolutely continuous invariant measure for τ.
The research of the second author was supported by NSERC and FCAR grants. 相似文献
19.
We consider the homogeneous Dirichlet problem in the unit disk K ⊂ R
2 for a general typeless differential equation of any even order 2 m, m ≥ 2, with constant complex coefficients whose characteristic equation has multiple roots ± i. For each value of multiplicity of the roots i and – i, we either formulate criteria of the nontrivial solvability of the problem or prove that the analyzed problem possesses solely
the trivial solution. A similar result generalizes the well-known Bitsadze examples to the case of typeless equations of any
even order. 相似文献
20.
This work presents guillotine constraints for two- and three-dimensional cutting problems. These problems look for a subset of rectangular items of maximum value that can be cut from a single rectangular container. Guillotine constraints seek to ensure that items are arranged in such a way that cuts from one edge of the container to the opposite edge completely separate them. In particular, we consider the possibility of 2, 3, and 4 cutting stages in a predefined sequence. These constraints are considered within a two-level iterative approach that combines the resolution of integer linear programming and constraint programming models. Experiments with instances of the literature are carried out, and the results show that the proposed approach can solve in less than 500 s approximately 60% and 50% of the instances for the two- and three-dimensional cases, respectively. For the two-dimensional case, in comparison with the recent literature, it was possible to improve the upper bound for 16% of the instances. 相似文献
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