Greedy algorithm

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

Primal-Dual RNC Approximation Algorithms for Set Cover and Covering Integer Programs

Abstract: We build on the classical greedy sequential set cover algorithm, in the spirit of the primal-dual schema, to obtain simple parallel approximation algorithms for the set cover problem and its generalizations. Our algorithms use randomization, and our randomized voting lemmas may be of independent interest. Fast parallel approximation algorithms were known before for set cover, though not for the generalizations considered in this paper.

Scheduling split intervals

Abstract: We consider the problem of scheduling jobs that are given as groups of non-intersecting segments on the real line. Each job Jj is associated with an interval, Ij, which consists of up to t segments, for some t ≥ 1, a positive weight, wj, and two jobs are in conflict if any of their segments intersect. Such jobs show up in a wide range of applications, including the transmission of continuous-media data, allocation of linear resources (e.g. bandwidth in linear processor arrays), and in computational biology/geometry. The objective is to schedule a subset of non-conflicting jobs of maximum total weight.In a single machine environment, our problem can be formulated as the problem of finding a maximum weight independent set in a t-interval graph (the special case of t = 1 is an ordinary interval graph). We show that, for t ≥ 2, this problem is APX-hard, even for highly restricted instances. Our main result is a 2t-approximation algorithm for general instances, based on a novel fractional version of the Local Ratio technique. Previously, the problem was considered only for proper union graphs, a restricted subclass of t-interval graphs, and the approximation factor achieved was (2t - 1 + 1/2t). A bi-criteria polynomial time approximation scheme (PTAS) is developed for the subclass of t-union graphs.In the online case, we consider uniform weight jobs that consist of at most two segments. We show that when the resulting 2-interval graph is proper, a simple greedy algorithm is 3-competitive, while any randomized algorithm has competitive ratio at least 2.5. For general instances, we give a randomized O(log2R)-competitive (or O((log R)2+e)-competitive) algorithm, where R is the known (unknown) ratio between the longest and the shortest segment in the input sequence.

On greedy construction of connected dominating sets in wireless networks

Abstract: Summary Since no fixed infrastructure and no centralized management present in wireless networks, a connected dominating set (CDS) of the graph representing the network is widely used as a virtual backbone. Constructing a minimum CDS is NP-hard. In this paper, we propose a new greedy algorithm, called S-MIS, with the help of Steiner tree that can construct a CDS within a factor of 4:8 þ ln5 from the optimal solution. We also introduce the distributed version of this algorithm. We prove that the proposed algorithm is better than the current best performance ratio which is 6.8. A simulation is conducted to compare S-MIS with its variation which is rS-MIS. The simulation shows that the sizes of the CDSs generated by S-MIS and rS-MIS are almost the same. Copyright # 2005 John Wiley & Sons, Ltd.

Wireless-Powered Communications With Non-Orthogonal Multiple Access

Abstract: We study a wireless-powered uplink communication system with non-orthogonal multiple access (NOMA), consisting of one base station and multiple energy harvesting users. More specifically, we focus on the individual data rate optimization and fairness improvement and we show that the formulated problems can be optimally and efficiently solved by either linear programming or convex optimization. In the provided analysis, two types of decoding order strategies are considered, namely fixed decoding order and time sharing . Furthermore, we propose an efficient greedy algorithm, which is suitable for the practical implementation of the time-sharing strategy. The simulation results illustrate that the proposed scheme outperforms the baseline orthogonal multiple access scheme. More specifically, it is shown that the NOMA offers a considerable improvement in throughput, fairness, and energy efficiency. Also, the dependence among system throughput, minimum individual data rate, and harvested energy is revealed, as well as an interesting tradeoff between rates and energy efficiency. Finally, the convergence speed of the proposed greedy algorithm is evaluated, and it is shown that the required number of iterations is linear with respect to the number of users.

Internal Node and Shortcut Based Routing with Guaranteed Delivery in Wireless Networks

Abstract: Several localized position based routing algorithms for wireless networks were described recently. In greedy routing algorithm (that has close performance to the shortest path algorithm, if successful), sender or node i>S currently holding the message i>m forwards i>m to one of its neighbors that is the closest to destination. The algorithm fails if i>S does not have any neighbor that is closer to destination than i>S. i>FACE algorithm guarantees the delivery of i>m if the network, modeled by unit graph, is connected. i>GFG algorithm combines greedy and i>FACE algorithms. Greedy algorithm is applied as long as possible, until delivery or a failure. In case of failure, the algorithm switches to i>FACE algorithm until a node closer to destination than last failure node is found, at which point greedy algorithm is applied again. Past traffic does not need to be memorized at nodes. In this paper we further improve the performance of i>GFG algorithm, by reducing its average hop count. First we improve the i>FACE algorithm by adding a sooner-back procedure for earlier escape from i>FACE mode. Then we perform a i>shortcut procedure at each forwarding node i>S. Node i>S uses the local information available to calculate as many hops as possible and forwards the packet to the last known hop directly instead of forwarding it to the next hop. The second improvement is based on the concept of dominating sets. Each node in the network is classified as internal or not, based on geographic position of its neighboring nodes. The network of internal nodes defines a connected dominating set, i.e., and each node must be either internal or directly connected to an internal node. In addition, internal nodes are connected. We apply several existing definitions of internal nodes, namely the concepts of intermediate, inter-gateway and gateway nodes. We propose to run i>GFG routing, enhanced by shortcut procedure, on the dominating set, except possibly the first and last hops. The performance of proposed algorithms is measured by comparing its average hop count with hop count of the basic i>GFG algorithm and the benchmark shortest path algorithm, and very significant improvements were obtained for low degree graphs. More precisely, we obtained localized routing algorithm that guarantees delivery and has very low excess in terms of hop count compared to the shortest path algorithm. The experimental data show that the length of additional path (in excess of shortest path length) can be reduced to about half of that of existing i>GFG algorithm.