We study nonlinear m-term approximation with regard to a redundant dictionary D in a Banach space. It is known that in the case of Hilbert space H the pure greedy algorithm (or, more generally, the weak greedy algorithm) provides for each f ∈ H and any dictionaryD an expansion into a series f = ∞ ∑ j=1 cj (f ) j (f ), j (f ) ∈ D, j = 1, 2, . . . with the Parseval property: ‖f ‖2 = ∑j |cj (f )|2...

Multiresolution surfaces are especially useful for fast rendering, real-time display and interactive manipulation of large and dense terrain surface models. This paper reviews major multiresolution terrain surface reconstruction techniques and analyses the corresponding data structures. We have proposed and implemented, based on Delaunay retriangulation, a greedy refinement algorithm with a str...

This paper gives an algorithm for finding the minimum weight tree having k edges in an edge weighted graph. The algorithm combines a search and optimization technique based on pheromone with a weight based greedy local optimization. Experimental results on a large set of problem instances show that this algorithm matches or surpasses other algorithms including an ant colony optimization algorit...

We present a polynomial time greedy algorithm that assigns proper wavelengths to a set of requests of maximum load L per directed ber link on a directed ber tree using at most 5=3L wavelengths. This improves previous results of 12, 10, 8, 9]. We also prove that no greedy algorithm can in general use less than 5=3L wavelengths for a set of requests of load L in a directed ber tree, and thus our ...

We consider load balancing of temporary tasks on m machines in the restricted assignment model. It is known that the best competitive ratio for this problem is Θ( √ m). This bound is not achieved by the greedy algorithm whose competitive ratio is known to be Ω(m 2 3 ). We give an alternative analysis to the greedy algorithm which is better than the known analysis for relatively small values of ...

Theorem 4.1.1 If OPT contains k sets, the greedy algorithm uses ≤ k(1 + ln nk ) sets. Proof: Let It be the sets selected by the greedy algorithm up to t iterations. Let nt be the number of uncovered elements at iteration t. Then nt = n− | ⋃ i∈It Si|, n0 = n, I0 = ∅. We claim that: Claim 4.1.2 nt ≤ (1− 1 k )nt−1 Proof: Let Jt = U\( ⋃ i∈It Si), then OPT covers Jt−1 with ≤ k sets. Because |Jt−1| =...

In many applications we are required to locate the most prominent group of vertices in a complex network. Group Betweenness Centrality can be used to evaluate the prominence of a group of vertices. Evaluating the Betweenness of every possible group in order to find the most prominent is not computationally feasible for large networks. In this paper we present two algorithms for finding the most...