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Greedy algorithm

About: Greedy algorithm is a research topic. Over the lifetime, 15347 publications have been published within this topic receiving 393945 citations.


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Proceedings ArticleDOI
23 Oct 2005
TL;DR: An O(log OPT) approximation is obtained for a generalization of the orienteering problem in which the profit for visiting each node may vary arbitrarily with time and the implications for the approximability of several basic optimization problems are interesting.
Abstract: Given an arc-weighted directed graph G = (V, A, /spl lscr/) and a pair of nodes s, t, we seek to find an s-t walk of length at most B that maximizes some given function f of the set of nodes visited by the walk. The simplest case is when we seek to maximize the number of nodes visited: this is called the orienteering problem. Our main result is a quasi-polynomial time algorithm that yields an O(log OPT) approximation for this problem when f is a given submodular set function. We then extend it to the case when a node v is counted as visited only if the walk reaches v in its time window [R(v), D(v)]. We apply the algorithm to obtain several new results. First, we obtain an O(log OPT) approximation for a generalization of the orienteering problem in which the profit for visiting each node may vary arbitrarily with time. This captures the time window problem considered earlier for which, even in undirected graphs, the best approximation ratio known [Bansal, N et al. (2004)] is O(log/sup 2/ OPT). The second application is an O(log/sup 2/ k) approximation for the k-TSP problem in directed graphs (satisfying asymmetric triangle inequality). This is the first non-trivial approximation algorithm for this problem. The third application is an O(log/sup 2/ k) approximation (in quasi-poly time) for the group Steiner problem in undirected graphs where k is the number of groups. This improves earlier ratios (Garg, N et al.) by a logarithmic factor and almost matches the inapproximability threshold on trees (Halperin and Krauthgamer, 2003). This connection to group Steiner trees also enables us to prove that the problem we consider is hard to approximate to a ratio better than /spl Omega/(log/sup 1-/spl epsi// OPT), even in undirected graphs. Even though our algorithm runs in quasi-poly time, we believe that the implications for the approximability of several basic optimization problems are interesting.

272 citations

Proceedings Article
03 Dec 2018
TL;DR: In this paper, the discriminative power of channels is considered and a greedy algorithm is proposed to perform channel selection and parameter optimization in an iterative way, which achieves state-of-the-art performance.
Abstract: Channel pruning is one of the predominant approaches for deep model compression. Existing pruning methods either train from scratch with sparsity constraints on channels, or minimize the reconstruction error between the pre-trained feature maps and the compressed ones. Both strategies suffer from some limitations: the former kind is computationally expensive and difficult to converge, whilst the latter kind optimizes the reconstruction error but ignores the discriminative power of channels. In this paper, we investigate a simple-yet-effective method called discrimination-aware channel pruning (DCP) to choose those channels that really contribute to discriminative power. To this end, we introduce additional discrimination-aware losses into the network to increase the discriminative power of intermediate layers and then select the most discriminative channels for each layer by considering the additional loss and the reconstruction error. Last, we propose a greedy algorithm to conduct channel selection and parameter optimization in an iterative way. Extensive experiments demonstrate the effectiveness of our method. For example, on ILSVRC-12, our pruned ResNet-50 with 30% reduction of channels outperforms the baseline model by 0.39% in top-1 accuracy.

269 citations

Journal ArticleDOI
TL;DR: In this article, the problem of designing spatially cohesive nature reserve systems that meet biodiversity objectives is formulated as a nonlinear integer programming problem, where the multiobjective function minimises a combination of boundary length, area and failed representation of the biological attributes we are trying to conserve.
Abstract: The problem of designing spatially cohesive nature reserve systems that meet biodiversity objectives is formulated as a nonlinear integer programming problem. The multiobjective function minimises a combination of boundary length, area and failed representation of the biological attributes we are trying to conserve. The task is to reserve a subset of sites that best meet this objective. We use data on the distribution of habitats in the Northern Territory, Australia, to show how simulated annealing and a greedy heuristic algorithm can be used to generate good solutions to such large reserve design problems, and to compare the effectiveness of these methods.

269 citations

Book ChapterDOI
16 Dec 1999
TL;DR: This work considers online routing strategies for routing between the vertices of embedded planar straight line graphs and proposes two deterministic memoryless routing strategies and a randomized memoryless strategy that works for all triangulations.
Abstract: We consider online routing strategies for routing between the vertices of embedded planar straight line graphs. Our results include (1) two deterministic memoryless routing strategies, one that works for all Delaunay triangulations and the other that works for all regular triangulations, (2) a randomized memoryless strategy that works for all triangulations, (3) an O(1) memory strategy that works for all convex subdivisions, (4) an O(1) memory strategy that approximates the shortest path in Delaunay triangulations, and (5) theoretical and experimental results on the competitiveness of these strategies.

268 citations

Journal ArticleDOI
TL;DR: The present paper unifies two studies of linear programming problems for which the greedy algorithm works, and establishes the converse of each theorem.

268 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023350
2022690
2021809
2020939
20191,006
2018967