We study approximation solutions for the densest k-subgraph problem (DS-k) on several classes of intersection graphs. We adopt the concept of σ-quasi elimination orders, introduced by Akcoglu et al. [?], generalizing the perfect elimination orders for chordal graphs, and develop a simple O(σ)-approximation technique for graphs admitting such a vertex order. This concept allows us to derive cons...

We present a simple family of algorithms for solving the Generalized Assignment Problem (GAP). Our technique is based on a novel combinatorial translation of any algorithm for the knapsack problem into an approximation algorithm for GAP. If the approximation ratio of the knapsack algorithm is α and its running time is O(f (N)), our algorithm guarantees a (1 + α)-approximation ratio, and it runs...

This paper presents a new practical approach to complex quadratic programming which solves the broad class of complex approximation problems employing finitization of semi-infinite formulations. The approximation problem may be general with arbitrarily complex basis functions. By using a new technique, the associated semi-infinite quadratic programming problem can be solved taking advantage of ...

The notion of a linguistic variable [17] together with fuzzy IF-THEN rules suggested a new formalism in the description of a man-machine interaction. Theoretical analysis of this formalism led to creation of a number of fuzzy theories: fuzzy logics, fuzzy measures, theory of t-norms etc. Successful applications of fuzzy IF-THEN rules in control, decision-making and expert systems [16] challenge...

We present in this work a technique for designing approximation schemes and its application to the discrete resource sharing problem (dRSSP ). We use the (classical) oracle formalism, in which a reliable oracle provides some information (usually called “a guess”) that helps to construct a good approximated solution. This oracle technique is sometimes called “partial enumeration” [ST07] or “outp...

This paper presents a new practical approach to semi-infinite complex Chebyshev approximation. By using a new technique, the general complex Chebyshev approximation problem can be solved with arbitrary base functions taking advantage of the numerical stability and efficiency of conventional linear programming software packages. Furthermore, the optimization procedure is simple to describe theor...

This article shows a relationship between two different approximation techniques: the support vector machines (SVM), proposed by V. Vapnik (1995) and a sparse approximation scheme that resembles the basis pursuit denoising algorithm (Chen, 1995; Chen, Donoho, and Saunders, 1995). SVM is a technique that can be derived from the structural risk minimization principle (Vapnik, 1982) and can be use...

This paper shows a relationship between two diierent approximation techniques: the Support Vector Machines (SVM), proposed by V. Vapnik (1995), and a sparse approximation scheme that resembles the Basis Pursuit De-Noising algorithm (Chen, 1995; Chen, Donoho and Saunders, 1995). SVM is a technique which can be derived from the Structural Risk Minimization Principle (Vapnik, 1982) and can be used...

This paper shows a relationship between two different approximation techniques: the Support Vector Machines (SVM), proposed by V. Vapnik (1995), and a sparse approximation scheme that resembles the Basis Pursuit De-Noising algorithm (Chen, 1995; Chen, Donoho and Saunders, 1995). SVM is a technique which can be derived from the Structural Risk Minimization Principle (Vapnik, 1982) and can be use...