Greedy algorithm

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

Minimizing service and operation costs of periodic scheduling

Abstract: We study the problem of scheduling activities of several types under the constraint that, at most, a fixed number of activities can be scheduled in any single time slot. Any given activity type is associated with a service cost and an operating cost that increases linearly with the number of time slots since the last service of this type. The problem is to find an optimal schedule that minimizes the long-run average cost per time slot. Applications of such a model are the scheduling of maintenance service to machines, multi-item replenishment of stock, and minimizing the mean response time in Broadcast Disks. Broadcast Disks recently gained a lot of attention because they were used to model backbone communications in wireless systems, Teletext systems, and Web caching in satellite systems. The first contribution of this paper is the definition of a general model that combines into one several important previous models. We prove that an optimal cyclic schedule for the general problem exists, and we establish the NP-hardness of the problem. Next, we formulate a nonlinear program that relaxes the optimal schedule and serves as a lower bound on the cost of an optimal schedule. We present an efficient algorithm for finding a near-optimal solution to the nonlinear program. We use this solution to obtain several approximation algorithms. 1 A 9/8 approximation for a variant of the problem that models the Broadcast Disks application. The algorithm uses some properties of “Fibonacci sequences.” Using this sequence, we present a 1.57-approximation algorithm for the general problem. 2 A simple randomized algorithm and a simple deterministic greedy algorithm for the problem. We prove that both achieve approximation factor of 2. To the best of our knowledge this is the first worst-case analysis of a widely used greedy heuristic for this problem.

Geometric spanners for routing in mobile networks

Abstract: We propose a new routing graph, the restricted Delaunay graph (RDG), for mobile ad hoc networks. Combined with a node clustering algorithm, the RDG can be used as an underlying graph for geographic routing protocols. This graph has the following attractive properties: 1) it is planar; 2) between any two graph nodes there exists a path whose length, whether measured in terms of topological or Euclidean distance, is only a constant times the minimum length possible; and 3) the graph can be maintained efficiently in a distributed manner when the nodes move around. Furthermore, each node only needs constant time to make routing decisions. We show by simulation that the RDG outperforms previously proposed routing graphs in the context of the Greedy perimeter stateless routing (GPSR) protocol. Finally, we investigate theoretical bounds on the quality of paths discovered using GPSR.

On finding graph clusterings with maximum modularity

Abstract: Modularity is a recently introduced quality measure for graph clusterings. It has immediately received considerable attention in several disciplines, and in particular in the complex systems literature, although its properties are not well understood. We study the problem of finding clusterings with maximum modularity, thus providing theoretical foundations for past and present work based on this measure. More precisely, we prove the conjectured hardness of maximizing modularity both in the general case and with the restriction to cuts, and give an Integer Linear Programming formulation. This is complemented by first insights into the behavior and performance of the commonly applied greedy agglomaration approach.

Contraflow Transportation Network Reconfiguration for Evacuation Route Planning

Abstract: Given a transportation network having source nodes with evacuees and destination nodes, we want to find a contraflow network configuration, i.e., ideal direction for each edge, to minimize evacuation time. Contraflow is considered a potential remedy to reduce congestion during evacuations in the context of homeland security and natural disasters (e.g., hurricanes). This problem is computationally challenging because of the very large search space and the expensive calculation of evacuation time on a given network. To our knowledge, this paper presents the first macroscopic approaches for the solution of contraflow network reconfiguration incorporating road capacity constraints, multiple sources, congestion factor, and scalability. We formally define the contraflow problem based on graph theory and provide a framework of computational workload to classify our approaches. A greedy heuristic is designed to produce high quality solutions with significant performance. A bottleneck relief heuristic is developed to deal with large numbers of evacuees. We evaluate the proposed approaches both analytically and experimentally using real world datasets. Experimental results show that our contraflow approaches can reduce evacuation time by 40% or more.

Evaluating improvements to a meta-heuristic search for constrained interaction testing

Abstract: Combinatorial interaction testing (CIT) is a cost-effective sampling technique for discovering interaction faults in highly-configurable systems. Constrained CIT extends the technique to situations where some features cannot coexist in a configuration, and is therefore more applicable to real-world software. Recent work on greedy algorithms to build CIT samples now efficiently supports these feature constraints. But when testing a single system configuration is expensive, greedy techniques perform worse than meta-heuristic algorithms, because greedy algorithms generally need larger samples to exercise the same set of interactions. On the other hand, current meta-heuristic algorithms have long run times when feature constraints are present. Neither class of algorithm is suitable when both constraints and the cost of testing configurations are important factors. Therefore, we reformulate one meta-heuristic search algorithm for constructing CIT samples, simulated annealing, to more efficiently incorporate constraints. We identify a set of algorithmic changes and experiment with our modifications on 35 realistic constrained problems and on a set of unconstrained problems from the literature to isolate the factors that improve performance. Our evaluation determines that the optimizations reduce run time by a factor of 90 and accomplish the same coverage objectives with even fewer system configurations. Furthermore, the new version compares favorably with greedy algorithms on real-world problems, and, though our modifications were aimed at constrained problems, it shows similar advantages when feature constraints are absent.