Topic
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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13 Jun 2015TL;DR: The main result is the first polynomial-time deterministic approximation algorithm for this problem, with an approximation ratio of 67/3, and a randomized version of the algorithm, with a ratio of 9+16√2/3.
Abstract: Communications in datacenter jobs (such as the shuffle operations in MapReduce applications) often involve many parallel flows, which may be processed simultaneously. This highly parallel structure presents new scheduling challenges in optimizing job-level performance objectives in data centers. Chowdhury and Stoica introduced the coflow abstraction to capture these communication patterns, and recently Chowdhury et al. developed effective heuristics to schedule coflows. In this paper, we consider the problem of efficiently scheduling coflows with release dates so as to minimize the total weighted completion time, which has been shown to be strongly NP-hard. Our main result is the first polynomial-time deterministic approximation algorithm for this problem, with an approximation ratio of 67/3, and a randomized version of the algorithm, with a ratio of 9+16√2/3. Our results use techniques from both combinatorial scheduling and matching theory, and rely on a clever grouping of coflows. We also run experiments on a Facebook trace to test the practical performance of several algorithms, including our deterministic algorithm. Our experiments suggest that simple algorithms provide effective approximations of the optimal, and that our deterministic algorithm has near-optimal performance.
110 citations
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14 Jun 2009TL;DR: A preemptive resume priority (PRP) M/G/1 queueing network model and a low-complexity greedy algorithm to select target channels to minimize the total service time with multiple spectrum handoffs are proposed.
Abstract: Spectrum handoff occurs when the primary users appear in the licensed band occupied by the secondary users. Spectrum handoff procedures aim to help the secondary users to vacate the occupied licensed spectrum and find suitable target channel to resume the unfinished transmission. In this paper, we discuss how to select the target channels to minimize the total service time with multiple spectrum handoffs. We propose a preemptive resume priority (PRP) M/G/1 queueing network model to evaluate total service time for various target channels selections. Then, we suggest a low-complexity greedy algorithm to select target channels. Numerical results show that a spectrum handoff scheme based on greedy selection strategy can reduce total service time compared to the randomly selection scheme.
110 citations
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16 Jun 2012TL;DR: A greedy-based approach to learn a compact and discriminative dictionary for sparse representation that yields dictionaries having the property that feature points from the same class have very similar sparse codes is presented.
Abstract: A greedy-based approach to learn a compact and discriminative dictionary for sparse representation is presented. We propose an objective function consisting of two components: entropy rate of a random walk on a graph and a discriminative term. Dictionary learning is achieved by finding a graph topology which maximizes the objective function. By exploiting the monotonicity and submodularity properties of the objective function and the matroid constraint, we present a highly efficient greedy-based optimization algorithm. It is more than an order of magnitude faster than several recently proposed dictionary learning approaches. Moreover, the greedy algorithm gives a near-optimal solution with a (1/2)-approximation bound. Our approach yields dictionaries having the property that feature points from the same class have very similar sparse codes. Experimental results demonstrate that our approach outperforms several recently proposed dictionary learning techniques for face, action and object category recognition.
110 citations
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TL;DR: An approximation algorithm similar to Christofides' algorithm for the traveling salesman problem is shown to possess the same worst-case bound of 3 2 when applied to the biconnectivity augmentation problem.
109 citations
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TL;DR: It is shown that phylogenetic diversity has an attractive mathematical property that ensures that it can be solved easily by the greedy algorithm: find a subset of the species of any given size k of maximal phylogenetic Diversity.
Abstract: Given a phylogenetic tree with leaves labeled by a collection of species, and with weighted edges, the "phylogenetic diversity" of any subset of the species is the sum of the edge weights of the minimal subtree connecting the species. This measure is relevant in biodiversity conservation where one may wish to compare different subsets of species according to how much evolutionary variation they encompass. In this note we show that phylogenetic diversity has an attractive mathematical property that ensures that we can solve the following problem easily by the greedy algorithm: find a subset of the species of any given size k of maximal phylogenetic diversity. We also describe an extension of this result that also allows weights to be assigned to species.
109 citations