Greedy algorithm

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

Connected Dominating Set in Sensor Networks and MANETs

Abstract: 3 Centralized CDS Construction 335 3.1 Guha and Khuller’s Algorithm . . . . . . . . . . . . . . . . . . . . . 336 3.2 Ruan’s Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 3.3 Cheng’s Greedy Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 340 3.4 Min’s Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341 3.5 Butenko’s Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 341

Generalized Proportional Fair Scheduling in Third Generation Wireless Data Networks

Abstract: In 3G data networks, network operators would like to balance system throughput while serving users in a fair manner. This is achieved using the notion of proportional fairness. However, so far, proportional fairness has been applied at each base station independently. Such an approach can result in non-Pareto optimal bandwidth allocation when considering the network as a whole. Therefore, it is important to consider proportional fairness in a network-wide context with user associations to base stations governed by optimizing a generalized proportional fairness objective. In this paper, we take the first step in formulating and studying this problem rigorously. We show that the general problem is NP-hard and it is also hard to obtain a close-to-optimal solution. We then consider a special case where multi-user diversity only depends on the number of users scheduled together. We propose efficient offline optimal algorithms and heuristic-based greedy online algorithms to solve this problem. Using detailed simulations based on the base station layout of a large service provider in the U.S., we show that our simple online algorithm, which assigns a newly arrived user to a base station that improves the generalized proportional fairness objective the most without changing existing users’ association, is very close to the offline optimal solution. The greedy algorithm can achieve significantly better throughput and fairness in heterogeneous user distributions, when compared to the approach that assigns a user to the base station with the best signal strength.

Rank Awareness in Joint Sparse Recovery

Abstract: In this paper we revisit the sparse multiple measurement vector (MMV) problem where the aim is to recover a set of jointly sparse multichannel vectors from incomplete measurements. This problem has received increasing interest as an extension of the single channel sparse recovery problem which lies at the heart of the emerging field of compressed sensing. However the sparse approximation problem has origins which include links to the field of array signal processing where we find the inspiration for a new family of MMV algorithms based on the MUSIC algorithm. We highlight the role of the rank of the coefficient matrix X in determining the difficulty of the recovery problem. We derive the necessary and sufficient conditions for the uniqueness of the sparse MMV solution, which indicates that the larger the rank of X the less sparse X needs to be to ensure uniqueness. We also show that the larger the rank of X the less the computational effort required to solve the MMV problem through a combinatorial search. In the second part of the paper we consider practical suboptimal algorithms for solving the sparse MMV problem. We examine the rank awareness of popular algorithms such as SOMP and mixed norm minimization techniques and show them to be rank blind in terms of worst case analysis. We then consider a family of greedy algorithms that are rank aware. The simplest such algorithm is a discrete version of MUSIC and is guaranteed to recover the sparse vectors in the full rank MMV case under mild conditions. We extend this idea to develop a rank aware pursuit algorithm that naturally reduces to Order Recursive Matching Pursuit (ORMP) in the single measurement case and also provides guaranteed recovery in the full rank multi-measurement case. Numerical simulations demonstrate that the rank aware algorithms are significantly better than existing algorithms in dealing with multiple measurements.

A heuristic nonlinear constructive method for distribution system reconfiguration

Abstract: This reconfiguration algorithm starts with all operable switches open, and at each step, closes the switch that results in the least increase in the objective function. The objective function is defined as incremental losses divided by incremental load served. A simplified loss formula is used to screen candidate switches, but a full load flow after each actual switch closing maintains accurate loss and constraint information. A backtracking option mitigates the algorithm's greedy search. This algorithm takes more computer time than other methods, but it models constraints and control action more accurately. A network load flow is used to provide a lower bound on the losses. The paper includes results on several test systems used by other authors.

Fast algorithms for maximizing submodular functions

Abstract: There has been much progress recently on improved approximations for problems involving submodular objective functions, and many interesting techniques have been developed. However, the resulting algorithms are often slow and impractical. In this paper we develop algorithms that match the best known approximation guarantees, but with significantly improved running times, for maximizing a monotone submodular function f: 2[n] → R+ subject to various constraints. As in previous work, we measure the number of oracle calls to the objective function which is the dominating term in the running time.Our first result is a simple algorithm that gives a (1--1/e -- e)-approximation for a cardinality constraint using O(n/e log n/e) queries, and a 1/(p + 2e + 1 + e)-approximation for the intersection of a p-system and e knapsack (linear) constraints using O (n/e2 log2n/e) queries. This is the first approximation for a p-system combined with linear constraints. (We also show that the factor of p cannot be improved for maximizing over a p-system.) The main idea behind these algorithms serves as a building block in our more sophisticated algorithms.Our main result is a new variant of the continuous greedy algorithm, which interpolates between the classical greedy algorithm and a truly continuous algorithm. We show how this algorithm can be implemented for matroid and knapsack constraints using O(n2) oracle calls to the objective function. (Previous variants and alternative techniques were known to use at least O(n4) oracle calls.) This leads to an O(n2/e4 log2n/e)-time (1--1/e -- e)-approximation for a matroid constraint. For a knapsack constraint, we develop a more involved (1--1/e -- e)-approximation algorithm that runs in time O(n2(1/e log n)poly(1/e)).