Greedy algorithm

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

Randomized 3D Geographic Routing

Abstract: We reconsider the problem of geographic routing in wireless ad hoc networks. We are interested in local, memoryless routing algorithms, i.e. each network node bases its routing decision solely on its local view of the network, nodes do not store any message state, and the message itself can only carry information about O(1) nodes. In geographic routing schemes, each network node is assumed to know the coordinates of itself and all adjacent nodes, and each message carries the coordinates of its target. Whereas many of the aspects of geographic routing have already been solved for 2D networks, little is known about higher-dimensional networks. It has been shown only recently that there is in fact no local memoryless routing algorithm for 3D networks that delivers messages deterministically. In this paper, we show that a cubic routing stretch constitutes a lower bound for any local memoryless routing algorithm, and propose and analyze several randomized geographic routing algorithms which work well for 3D network topologies. For unit ball graphs, we present a technique to locally capture the surface of holes in the network, which leads to 3D routing algorithms similar to the greedy-face-greedy approach for 2D networks.

Optimal Resource Allocation in Simultaneous Cooperative Spectrum Sensing and Energy Harvesting for Multichannel Cognitive Radio

Abstract: In this paper, a simultaneous cooperative spectrum sensing and energy harvesting model is proposed to improve the transmission performance of the multichannel cognitive radio. The frame structure is divided into sensing slot and transmission slot. In the sensing slot, the secondary user (SU) splits the subchannels into two subchannel sets, one for sensing the primary user (PU) by multichannel cooperative spectrum sensing and the other one for collecting the radio frequency energy of the PU signal and noise by multichannel energy harvesting. In the transmission slot, the harvested energy is supplied to compensate the sensing energy loss in order to guarantee the throughput. We have formulated the resource allocation of the proposed model as a class of optimization problems, which maximize aggregate throughput, harvested energy, and energy efficiency of the SU over all the subchannels through jointly optimizing subchannel set, sensing time, and transmission power, respectively. To achieve the sub-optimal solutions to the optimization problems, we have proposed the subchannel allocation algorithm and the joint optimization algorithm of sensing time and transmission power based on the Greedy algorithm and the alternating direction optimization. The stopping criteria of SU is described, when the PU is not present but the harvested energy is not enough. The simulation results are presented to demonstrate the validity and predominance of our proposed algorithms.

Maximal lifetime scheduling in sensor surveillance networks

Abstract: This paper addresses the maximal lifetime scheduling problem in sensor surveillance networks. Given a set of sensors and targets in a Euclidean plane, a sensor can watch only one target at a time, our task is to schedule sensors to watch targets, such that the lifetime of the surveillance system is maximized, where the lifetime is the duration that all targets are watched. We propose an optimal solution to find the target watching schedule for sensors that achieves the maximal lifetime. Our solution consists of three steps: 1) computing the maximal lifetime of the surveillance system and a workload matrix by using linear programming techniques; 2) decomposing the workload matrix into a sequence of schedule matrices that can achieve the maximal lifetime; 3) obtaining a target watching timetable for each sensor based on the schedule matrices. Simulations have been conducted to study the complexity of our proposed method and to compare with the performance of a greedy method.

Optimal greedy algorithms for indifference graphs

Abstract: A fundamental problem in social sciences and management is understanding and predicting decisions made by individuals, various groups, or the society as a whole. In this context, one important concept is the notion of indifference. We characterize the class of indifference graphs, that is, graphs which arise in the process of quantifying indifference relations. In particular, we show that these graphs are characterized by the existence of a special ordering of their vertices. As it turns out, this ordering leads naturally to optimal greedy algorithms for a number of computational problems, including coloring, finding a shortest path between two vertices, computing a maximum matching, the center, and a Hamiltonian path.

Linear approximation of shortest superstrings

Abstract: We consider the following problem: given a collection of strings s1,…, sm, find the shortest string s such that each si appears as a substring (a consecutive block) of s. Although this problem is known to be NP-hard, a simple greedy procedure appears to do quite well and is routinely used in DNA sequencing and data compression practice, namely: repeatedly merge the pair of (distinct) strings with maximum overlap until only one string remains. Let n denote the length of the optimal superstring. A common conjecture states that the above greedy procedure produces a superstring of length O(n) (in fact, 2n), yet the only previous nontrivial bound known for any polynomial-time algorithm is a recent O(n log n) result.We show that the greedy algorithm does in fact achieve a constant factor approximation, proving an upper bound of 4n. Furthermore, we present a simple modified version of the greedy algorithm that we show produces a superstring of length at most 3n. We also show the superstring problem to be MAXSNP-hard, which implies that a polynomial-time approximation scheme for this problem is unlikely.