Greedy algorithm

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

Decision trees for entity identification: approximation algorithms and hardness results

Abstract: We consider the problem of constructing decision trees for entity identification from a given relational table. The input is a table containing information about a set of entities over a fixed set of attributes and a probability distribution over the set of entities that specifies the likelihood of the occurrence of each entity. The goal is to construct a decision tree that identifies each entity unambiguously by testing the attribute values such that the average number of tests is minimized. This classical problem finds such diverse applications as efficient fault detection, species identification in biology, and efficient diagnosis in the field of medicine. Prior work mainly deals with the special case where the input table is binary and the probability distribution over the set of entities is uniform. We study the general problem involving arbitrary input tables and arbitrary probability distributions over the set of entities. We consider a natural greedy algorithm and prove an approximation guarantee of O(rK • log N), where N is the number of entities and K is the maximum number of distinct values of an attribute. The value rK is a suitably defined Ramsey number, which is at most log K. We show that it is NP-hard to approximate the problem within a factor of Ω(log N), even for binary tables (i.e. K=2). Thus, for the case of binary tables, our approximation algorithm is optimal up to constant factors (since r2=2). In addition, our analysis indicates a possible way of resolving a Ramsey-theoretic conjecture by Erdos.

Dynamic allocation indices for restless projects and queueing admission control: a polyhedral approach

Abstract: This paper develops a polyhedral approach to the design, analysis, and computation of dynamic allocation indices for scheduling binary-action (engage/rest) Markovian stochastic projects which can change state when rested (restless bandits (RBs)), based on partial conservation laws (PCLs). This extends previous work by the author [J. Nino-Mora (2001): Restless bandits, partial conservation laws and indexability. Adv. Appl. Probab. 33, 76–98], where PCLs were shown to imply the optimality of index policies with a postulated structure in stochastic scheduling problems, under admissible linear objectives, and they were deployed to obtain simple sufficient conditions for the existence of Whittle's (1988) RB index (indexability), along with an adaptive-greedy index algorithm. The new contributions include: (i) we develop the polyhedral foundation of the PCL framework, based on the structural and algorithmic properties of a new polytope associated with an accessible set system -extended polymatroid}); (ii) we present new dynamic allocation indices for RBs, motivated by an admission control model, which extend Whittle's and have a significantly increased scope; (iii) we deploy PCLs to obtain both sufficient conditions for the existence of the new indices (PCL-indexability), and a new adaptive-greedy index algorithm; (iv) we interpret PCL-indexability as a form of the classic economics law of diminishing marginal returns, and characterize the index as an optimal marginal cost rate; we further solve a related optimal constrained control problem; (v) we carry out a PCL-indexability analysis of the motivating admission control model, under time-discounted and long-run average criteria; this gives, under mild conditions, a new index characterization of optimal threshold policies; and (vi) we apply the latter to present new heuristic index policies for two hard queueing control problems: admission control and routing to parallel queues; and scheduling a multiclass make-to-stock queue with lost sales, both under state-dependent holding cost rates and birth-death dynamics.

Analysis of a switch matrix for an SS/TDMA system

Abstract: Time slot scheduling problem for a satellite switched/time-division multiple access (SS/TDMA) system is discussed and an algorithm called "Greedy Algorithm" is presented. This algorithm guarantees a most efficient utilization of a frame period with n2- n (n is the number of beams) number of switchings at most. Another problem discussed in this paper is the choice of the type of microwave switch matrix to be put on board the satellite. A switch-matrix structure called rearrangeable multistage matrix is shown to have high reliability and low-insertion-loss characteristics. Also brief discussions are made on the experimental results of an engineering model SS/TDMA system.

Stochastic programming for nurse assignment

Abstract: We present a brief overview of four phases of nurse planning. For the last phase, which assigns nurses to patients, a stochastic integer programming model is developed. A Benders' decomposition approach is proposed to solve this problem, and a greedy algorithm is employed to solve the recourse subproblem. To improve the efficiency of the algorithm, we introduce sets of valid inequalities to strengthen a relaxed master problem. Computational results are provided based upon data from Baylor Regional Medical Center in Grapevine, Texas. Finally, areas of future research are discussed.

QoS Routing in Smart Grid

Abstract: Smart grid is an emerging technology which is able to control the power load via price signaling. The communication between the power supplier and power customers is a key issue in smart grid. Performance degradation like delay or outage may cause significant impact on the stability of the pricing based control and thus the reward of smart grid. Therefore, a QoS mechanism is proposed for the communication system in smart grid, which incorporates the derivation of QoS requirement and applies QoS routing in the communication network. For deriving the QoS requirement, the dynamics of power load and the load-price mapping are studied. The corresponding impacts of different QoS metrics like delay are analyzed. Then, the QoS is derived via an optimization problem that maximizes the total revenue. Based on the derived QoS requirement, a simple greedy QoS routing algorithm is proposed for the requirement of high speed routing in smart grid. It is also proven that the proposed greedy algorithm is a $K$-approximation. Numerical simulation shows that the proposed mechanism and algorithm can effectively derive and secure the communication QoS in smart grid.