Greedy algorithm

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

An improved iterated greedy algorithm for the no-wait flow shop scheduling problem with makespan criterion

Abstract: An improved iterated greedy algorithm (IIGA) is proposed in this paper to solve the no-wait flow shop scheduling problem with the objective to minimize the makespan. In the proposed IIGA, firstly, a speed-up method for the insert neighborhood is developed to evaluate the whole insert neighborhood of a single solution with (n − 1)2 neighbors in time O(n 2), where n is the number of jobs; secondly, an improved Nawaz-Enscore-Ham (NEH) heuristic is presented for constructing solutions in the initial stage and searching process; thirdly, a simple local search algorithm based on the speed-up method is incorporated into the iterated greedy algorithm to perform exploitation. The computational results based on some well-known benchmarks show that the proposed IIGA can obtain results better than those from some existing approaches in the literature.

Some Results on Greedy Embeddings in Metric Spaces

Abstract: Geographic Routing is a family of routing algorithms that uses geographic point locations as addresses for the purposes of routing. Such routing algorithms have proven to be both simple to implement and heuristically effective when applied to wireless sensor networks. Greedy Routing is a natural abstraction of this model in which nodes are assigned virtual coordinates in a metric space, and these coordinates are used to perform point-to-point routing. Here we resolve a conjecture of Papadimitriou and Ratajczak that every 3-connected planar graph admits a greedy embedding into the Euclidean plane. This immediately implies that all 3-connected graphs that exclude K 3,3 as a minor admit a greedy embedding into the Euclidean plane. We also prove a combinatorial condition that guarantees nonembeddability. We use this result to construct graphs that can be greedily embedded into the Euclidean plane, but for which no spanning tree admits such an embedding.

Local and global recoding methods for anonymizing set-valued data

Abstract: In this paper, we study the problem of protecting privacy in the publication of set-valued data. Consider a collection of supermarket transactions that contains detailed information about items bought together by individuals. Even after removing all personal characteristics of the buyer, which can serve as links to his identity, the publication of such data is still subject to privacy attacks from adversaries who have partial knowledge about the set. Unlike most previous works, we do not distinguish data as sensitive and non-sensitive, but we consider them both as potential quasi-identifiers and potential sensitive data, depending on the knowledge of the adversary. We define a new version of the k-anonymity guarantee, the k m -anonymity, to limit the effects of the data dimensionality, and we propose efficient algorithms to transform the database. Our anonymization model relies on generalization instead of suppression, which is the most common practice in related works on such data. We develop an algorithm that finds the optimal solution, however, at a high cost that makes it inapplicable for large, realistic problems. Then, we propose a greedy heuristic, which performs generalizations in an Apriori, level-wise fashion. The heuristic scales much better and in most of the cases finds a solution close to the optimal. Finally, we investigate the application of techniques that partition the database and perform anonymization locally, aiming at the reduction of the memory consumption and further scalability. A thorough experimental evaluation with real datasets shows that a vertical partitioning approach achieves excellent results in practice.

VNR Algorithm: A Greedy Approach for Virtual Networks Reconfigurations

Abstract: In this paper we address the problem of virtual network reconfiguration. In our previous work on virtual network embedding strategies, we found that most virtual network rejections were caused by bottlenecked substrate links while peak resource use is equal to 18%. These observations lead us to propose a new greedy Virtual Network Reconfiguration algorithm, VNR. The main aim of our proposal is to 'tidy up' substrate network in order to minimise the number of overloaded substrate links, while also reducing the cost of reconfiguration. We compare our proposal with the related reconfiguration strategy VNA-Periodic, both of them are incorporated in the best existing embedding strategies VNE-AC and VNE-Greedy in terms of rejection rate. The results obtained show that VNR outperforms VNA-Periodic. Indeed, our research shows that the performances of VNR do not depend on the virtual network embedding strategy. Moreover, VNR minimises the rejection rate of virtual network requests by at least 83% while the cost of reconfiguration is lower than with VNA-Periodic.

Guarantees for Greedy maximization of non-submodular functions with applications

Abstract: We investigate the performance of the standard GREEDY algorithm for cardinality constrained maximization of non-submodular nondecreasing set functions. While there are strong theoretical guarantees on the performance of GREEDY for maximizing submodular functions, there are few guarantees for non-submodular ones. However, GREEDY enjoys strong empirical performance for many important non-submodular functions, e.g., the Bayesian A-optimality objective in experimental design. We prove theoretical guarantees supporting the empirical performance. Our guarantees are characterized by a combination of the (generalized) curvature α and the sub-modularity ratio γ. In particular, we prove that GREEDY enjoys a tight approximation guarantee of 1/α (1 - e-γα) for cardinality constrained maximization. In addition, we bound the submod-ularity ratio and curvature for several important real-world objectives, including the Bayesian A-optimality objective, the determinantal function of a square submatrix and certain linear programs with combinatorial constraints. We experimentally validate our theoretical findings for both synthetic and real-world applications.