We propose two new algorithms to improve greedy sampling of high-dimensional functions. While the techniques have a substantial degree of generality, we frame the discussion in the context of methods for empirical interpolation and the development of reduced basis techniques for high-dimensional parametrized functions. The first algorithm, based on a saturation assumption of the error in the gr...

As a useful data mining technique biclustering identifies local patterns from gene expression data. A bicluster of a gene expression dataset is a subset of genes which exhibit similar expression patterns along a subset of conditions. In this paper a new method is introduced based on greedy search algorithm combined with the evolutionary technique particle swarm optimization for the identificati...

In the unweighted set-cover problem we are given a set of elements E = {e1, e2, . . . , en} and a collection F of subsets of E. The problem is to compute a sub-collection SOL ⊆F such that ⋃ Sj∈SOL Sj = E and its size |SOL| is minimized. When |S| ≤ k for all S ∈ F we obtain the unweighted k-set cover problem. It is well known that the greedy algorithm is an Hk-approximation algorithm for the unw...

We investigate the greedy algorithm for the shortest common superstring problem. We show that the length of the greedy superstring is upper-bounded by the sum of the lengths of an optimal superstring and an optimal cycle cover, provided the greedy algorithm happens to merge the strings in a particular way. Thus, when restricting inputs correspondingly, we verify the well known greedy conjecture...

Generalizing the idea of the Lovász extension of a set function and the discrete Choquet integral, we introduce a combinatorial model that allows us to define and analyze matroid-type greedy algorithms. The model is based on a real-valued function v on a (finite) family of sets which yields the constraints of a combinatorial linear program. Moreover, v gives rise to a ranking and selection proc...

We consider the minimization version of the multi-dimensional knapsack problem with bounded integer variables. We propose a greedy approximation algorithm that runs in O(mn) time and has a guarantee of m + 1, where n is the number of items and m is the number of knapsack constraints. The guarantee of the algorithm can be improved in case of easy coefficients in the constraints associated with s...

We show that the left-greedy algorithm is a better algorithm than the right-greedy algorithm for sorting permutations using t stacks in series when t > 1. We also supply a method for constructing some permutations that can be sorted by t stacks in series and from this get a lower bound on the number of permutations of length n that are sortable by t stacks in series. Finally we show that the le...

In this paper we consider the classical Connected Dominating Set (CDS) problem. Twenty years ago, Guha and Khuller developed two algorithms for this problem a centralized greedy approach with an approximation guarantee ofH(∆)+2, and a local greedy approach with an approximation guarantee of 2(H(∆) + 1) (where H() is the harmonic function, and ∆ is the maximum degree in the graph). A local greed...

Cellular networks are facing severe traffic overloads due to the proliferation of smart handheld devices and traffic hungry applications. This paper tries to offload the cellular network traffic through Opportunistic Communications and Social Participation formed by the short-range communication technologies in the smart phones (e.g., Wi-Fi, Bluetooth). We design an Enhanced Greedy algorithm fo...

Greedy algorithms are used in solving a diverse set of problems in small computation time. However, for solving problems using greedy approach, it must be proved that the greedy strategy applies. The greedy approach relies on selection of optimal choice at a local level reducing the problem to a single sub problem, which actually leads to a globally optimal solution. Finding a maximal set from ...