On an approximation measure founded on the links between optimization and polynomial approximation theory

Demange, Marc; Paschos, Vangélis Th.

doi:10.1016/0304-3975(95)00060-7

Cited by 73 publications

(75 citation statements)

References 7 publications

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“…Nevertheless, our branch-and-bound procedure is not destined to be embedimation ratio (recall that differential approximation is concerned with how far the value of a solution is from the worst possible value [11]) or as a conventional approximation ratio [12] for the maximization problem complementary to the PMP problem which asks to maximize the sum of the costs of the moves which are not interrupted.…”

Section: Resultsmentioning

confidence: 99%

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On a resource-constrained scheduling problem with application to distributed systems reconfiguration

Sirdey

Carlier

Kerivin

et al. 2007

European Journal of Operational Research

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International audienceThis paper is devoted to the study of a resource-constrained scheduling problem, the Process Move Programming problem, which arises in relation to the operability of certain high availability real-time distributed systems. Informally, this problem consists, starting from an arbitrary initial distribution of processes on the processors of a distributed system, in finding the least disruptive sequence of operations (non-impacting process migrations or temporary process interruptions) at the end of which the system ends up in another predefined arbitrary state. The main constraint is that the capacity of the processors must not be exceeded during the reconfiguration. After a brief survey of the literature, we prove the NP-hardness of the problem and exhibit a few polynomial special cases. We then present a branch-and-bound algorithm for the general case along with computational results demonstrating its practical relevance

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Section: Resultsmentioning

confidence: 99%

“…Also, computationally cheaper, but weaker, lower bounds can be obtained from any upper bound for problem (11), the so-called Dantzig bound obtained by solving the linear relaxation of the knapsack problem would be an example.…”

Section: Lower Boundsmentioning

confidence: 99%

On a resource-constrained scheduling problem with application to distributed systems reconfiguration

Sirdey

Carlier

Kerivin

et al. 2007

European Journal of Operational Research

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“…We use (6), (7), and (8) to upper-bound the left side of inequality (9). We have By expressing inequalities (1)- (5) and (11) in standard form, we obtain our parameterized LP lemma.…”

Section: This Naturally Corresponds To a Star Set Cover O For (V S) mentioning

confidence: 99%

“…The approximation ratio of a solution for complementary set cover can be thought of as comparing the "distance" of a solution for set cover from the worst possible solution (i.e., the one that uses n sets to cover the elements) to the distance of the best solution of the worst possible one. This yields an alternative performance measure for the analysis of approximation algorithms; such measures have been considered for many combinatorial optimization problems in the context of differential approximation algorithms [10,9] or z-approximations [16] (see also [3,4]). Duh and Fürer [11] also consider the application of their algorithm on instances of complementary set cover in which the collection of sets is not given explicitly.…”

Section: Introductionmentioning

confidence: 99%

An Improved Approximation Bound for Spanning Star Forest and Color Saving

Athanassopoulos

Caragiannis

Kaklamanis

et al. 2009

Mathematical Foundations of Computer Science 2009

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Abstract. We present a simple algorithm for the maximum spanning star forest problem. We take advantage of the fact that the problem is a special case of complementary set cover and we adapt an algorithm of Duh and Fürer in order to solve it. We prove that this algorithm computes 193/240 ≈ 0.804-approximate spanning star forests; this result improves a previous lower bound of 0.71 by Chen et al. Although the algorithm is purely combinatorial, our analysis defines a linear program that uses a parameter f and which is feasible for values of the parameter f not smaller than the approximation ratio of the algorithm. The analysis is tight and, interestingly, it also applies to complementary versions of set cover such as color saving; it yields the same approximation guarantee of 193/240 that marginally improves the previously known upper bound of Duh and Fürer. We also show that, in general, a natural class of local search algorithms do not provide better than 1/2-approximate spanning star forests.

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“…The quality of A is expressed by the means of approximation ra-tios that somehow compare the approximate value to the optimum one. So far, two measures stand out from the literature: the standard ratio [2] (the most widely used) and the differential ratio [3,4,7,10]. The standard ratio is defined by ρ Π (I, A) = apx Π (I)/opt Π (I) if Π is a maximization problem, by ρ Π (I, A) = opt Π (I)/apx Π (I) otherwise, whereas the differential ratio is defined by δ Π (I, A)(wor Π (I) − apx Π (I))/(wor Π (I) − opt Π (I)).…”

Section: Introductionmentioning

confidence: 99%

Fundamentals of Computation Theory

Liśkiewicz¹,

Reischuk²

2005

Lecture Notes in Computer Science

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We present several new standard and differential approximation results for the P 4 -partition problem using the Hassin and Rubinstein' algorithm (Information Processing Letters, 63: 63-67, 1997). Those results concern both minimization and maximization versions of the problem. However, the main point of this paper lies on the establishment it does of the robustness of this algorithm, in the sense that this latter provides good quality solutions, whatever version of the problem is addressed, whatever approximation framework is considered in order to evaluate the approximate solutions.

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On an approximation measure founded on the links between optimization and polynomial approximation theory

Cited by 73 publications

References 7 publications

On a resource-constrained scheduling problem with application to distributed systems reconfiguration

On a resource-constrained scheduling problem with application to distributed systems reconfiguration

An Improved Approximation Bound for Spanning Star Forest and Color Saving

Fundamentals of Computation Theory

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