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1.
Yossi Azar Leah Epstein Yossi Richter Gerhard J Woeginger 《Journal of Algorithms in Cognition, Informatics and Logic》2004,52(2):2577
A major drawback in optimization problems and in particular in scheduling problems is that for every measure there may be a different optimal solution. In many cases the various measures are different ℓp norms. We address this problem by introducing the concept of an all-norm ρ-approximation algorithm, which supplies one solution that guarantees ρ-approximation to all ℓp norms simultaneously. Specifically, we consider the problem of scheduling in the restricted assignment model, where there are m machines and n jobs, each job is associated with a subset of the machines and should be assigned to one of them. Previous work considered approximation algorithms for each norm separately. Lenstra et al. [Math. Program. 46 (1990) 259–271] showed a 2-approximation algorithm for the problem with respect to the ℓ∞ norm. For any fixed ℓp norm the previously known approximation algorithm has a performance of θ(p). We provide an all-norm 2-approximation polynomial algorithm for the restricted assignment problem. On the other hand, we show that for any given ℓp norm (p>1) there is no PTAS unless P=NP by showing an APX-hardness result. We also show for any given ℓp norm a FPTAS for any fixed number of machines. 相似文献
2.
Explicit expressions for all the 3n+2 primitive idempotents in the ring Rpnq=GF(ℓ)[x]/(xpnq−1), where p,q,ℓ are distinct odd primes, ℓ is a primitive root modulo pn and q both,
, are obtained. The dimension, generating polynomials and the minimum distance of the minimal cyclic codes of length pnq over GF(ℓ) are also discussed. 相似文献
3.
Given a set of strings U={T1,T2,…,Tℓ}, the longest common repeat problem is to find the longest common substring that appears at least twice in each string of U. We also consider reversed and reverse-complemented repeats as well as normal repeats. We present a linear time algorithm for the longest common repeat problem. 相似文献
4.
Let denote the set of continuous n×n matrices on an interval . We say that is a nontrivial k-involution if where ζ=e-2πi/k, d0+d1++dk-1=n, and with . We say that is R-symmetric if R(t)A(t)R-1(t)=A(t), , and we show that if A is R-symmetric then solving x′=A(t)x or x′=A(t)x+f(t) reduces to solving k independent dℓ×dℓ systems, 0ℓk-1. We consider the asymptotic behavior of the solutions in the case where . Finally, we sketch analogous results for linear systems of difference equations. 相似文献
5.
Amin Coja-Oghlan Konstantinos Panagiotou Angelika Steger 《Journal of Combinatorial Theory, Series B》2008,98(5):980-993
In this paper we consider the classical Erdős–Rényi model of random graphs Gn,p. We show that for p=p(n)n−3/4−δ, for any fixed δ>0, the chromatic number χ(Gn,p) is a.a.s. ℓ, ℓ+1, or ℓ+2, where ℓ is the maximum integer satisfying 2(ℓ−1)log(ℓ−1)p(n−1). 相似文献
6.
In this paper, we study inverse optimization for linearly constrained convex separable programming problems that have wide applications in industrial and managerial areas. For a given feasible point of a convex separable program, the inverse optimization is to determine whether the feasible point can be made optimal by adjusting the parameter values in the problem, and when the answer is positive, find the parameter values that have the smallest adjustments. A sufficient and necessary condition is given for a feasible point to be able to become optimal by adjusting parameter values. Inverse optimization formulations are presented with ℓ1 and ℓ2 norms. These inverse optimization problems are either linear programming when ℓ1 norm is used in the formulation, or convex quadratic separable programming when ℓ2 norm is used. 相似文献
7.
Amihood Amir Yonatan Aumann Gad M. Landau Moshe Lewenstein Noa Lewenstein 《Journal of Algorithms in Cognition, Informatics and Logic》2000,37(2):247
Let a text string T of n symbols and a pattern string P of m symbols from alphabet Σ be given. A swapped version T′ of T is a length n string derived from T by a series of local swaps (i.e., t′ℓ ← tℓ + 1 and t′ℓ + 1 ← tℓ), where each element can participate in no more than one swap. The pattern matching with swaps problem is that of finding all locations i for which there exists a swapped version T′ of T with an exact matching of P in location i of T′. It has been an open problem whether swapped matching can be done in less than O(nm) time. In this paper we show the first algorithm that solves the pattern matching with swaps problem in time o(nm). We present an algorithm whose time complexity is O(nm1/3 log m log σ) for a general alphabet Σ, where σ = min(m,Σ). 相似文献
8.
A. I. Khrabrov 《Journal of Mathematical Sciences》2005,129(4):4040-4048
We study classical, modified, and weak Banach-Mazur distances between sums of the spaces ℓ
n
p
. We calculate explicitly the classical and weak Banach-Mazur distances between sums of the spaces ℓ
n
p
and obtain bounds for ratios of distances between sums of the spaces ℓ
n
p
. Bibliography: 14 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 303, 2003, pp. 203–217. 相似文献
9.
For a bounded integer ℓ, we wish to color all edges of a graph G so that any two edges within distance ℓ have different colors. Such a coloring is called a distance-edge-coloring or an ℓ-edge-coloring of G. The distance-edge-coloring problem is to compute the minimum number of colors required for a distance-edge-coloring of a given graph G. A partial k-tree is a graph with tree-width bounded by a fixed constant k. We first present a polynomial-time exact algorithm to solve the problem for partial k-trees, and then give a polynomial-time 2-approximation algorithm for planar graphs. 相似文献
10.
Thomas Weigel 《Archiv der Mathematik》2005,85(1):55-69
Any morphism
of profinite groups has maximal ℓ-Frattini quotients
is an ℓ-Frattini extension and β is a surjective morphism of profinite groups for which every minimal finite non-trivial ℓ-embedding problem is not weakly solvable. In this paper the case is studied where Ĝ
Ĝ is a weakly-orientable ℓ-Poincaré duality group of dimension 2 and where A is a finite group whose order is divisible by ℓ. This analysis can be applied for the study of modular towers (Theorem A, Remark 1.2). It is shown that the existence of finite maximal ℓ-Frattini quotients is controlled by an integer r
ℓ(A) (Theorem B). In the final section we study properties of the morphism ϕ which imply that for every maximal ℓ-Frattini quotient (π, β), the profinite group B itself is a weakly-orientable ℓ-Poincaré duality group of dimension 2 (Theorem C).Received: 17 January 2005; revised: 21 March 2005 相似文献
11.
A. G. Ramm 《Applied Mathematics Letters》1988,1(3)
Let·(σ(x)u)= 0 in D R3, where D is a bounded domain with a smooth boundary. Suppose that σ ≥ m> 0, σ H3(D), where Hℓ is the Sobolev space. Let the set {u, σuN} be given on Γ for all u H3/2(Γ), where uN is the normal derivative of u on Γ. 相似文献
12.
《European Journal of Combinatorics》2002,23(8):1061
A finite connected graph is called an ℓ1-graph if it can be isometrically embedded into the space ℓ1. We complete the classification of pairs of complementaryℓ1 -graphs started by Deza and Huang, and continued by Shpectorov. 相似文献
13.
Gad M. Landau Michal Ziv-Ukelson 《Journal of Algorithms in Cognition, Informatics and Logic》2001,41(2):338
The Common Substring Alignment Problem is defined as follows: Given a set of one or more strings S1, S2 … Sc and a target string T, Y is a common substring of all strings Si, that is, Si = BiYFi. The goal is to compute the similarity of all strings Si with T, without computing the part of Y again and again. Using the classical dynamic programming tables, each appearance of Y in a source string would require the computation of all the values in a dynamic programming table of size O(nℓ) where ℓ is the size of Y. Here we describe an algorithm which is composed of an encoding stage and an alignment stage. During the first stage, a data structure is constructed which encodes the comparison of Y with T. Then, during the alignment stage, for each comparison of a source Si with T, the pre-compiled data structure is used to speed up the part of Y. We show how to reduce the O(nℓ) alignment work, for each appearance of the common substring Y in a source string, to O(n)-at the cost of O(nℓ) encoding work, which is executed only once. 相似文献
14.
Upper estimates for the order of Gâteaux smoothness of bump functions in Orlicz spaces ℓM(Γ) and Lorentz spaces d(w, p, Γ), Γ uncountable, are obtained. 相似文献
15.
A hypergraph G=(V,E) is (k,ℓ)-sparse if no subset V′V spans more than k|V′|−ℓ hyperedges. We characterize (k,ℓ)-sparse hypergraphs in terms of graph theoretic, matroidal and algorithmic properties. We extend several well-known theorems of Haas, Lovász, Nash-Williams, Tutte, and White and Whiteley, linking arboricity of graphs to certain counts on the number of edges. We also address the problem of finding lower-dimensional representations of sparse hypergraphs, and identify a critical behavior in terms of the sparsity parameters k and ℓ. Our constructions extend the pebble games of Lee and Streinu [A. Lee, I. Streinu, Pebble game algorithms and sparse graphs, Discrete Math. 308 (8) (2008) 1425–1437] from graphs to hypergraphs. 相似文献
16.
We present a condition on the matrix of an underdetermined linear system which guarantees that the solution of the system with minimal ℓq-quasinorm is also the sparsest one. This generalizes, and slightly improves, a similar result for the ℓ1-norm. We then introduce a simple numerical scheme to compute solutions with minimal ℓq-quasinorm, and we study its convergence. Finally, we display the results of some experiments which indicate that the ℓq-method performs better than other available methods. 相似文献
17.
In this paper, the authors study the asymptotic behavior of solutions of second-order neutral type difference equations of the form
Δ2(yn+pyn−k)+f(n,yn−ℓ)=0,n