Greedy algorithm

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

Towards Efficient Geographic Routing in Urban Vehicular Networks

Abstract: Vehicular ad hoc networks (VANETs) have received considerable attention in recent times. Multihop data delivery between vehicles is an important aspect for the support of VANET-based applications. Although data dissemination and routing have extensively been addressed, many unique characteristics of VANETs, together with the diversity in promising applications, offer newer research challenges. This paper introduces the improved greedy traffic-aware routing protocol (GyTAR), which is an intersection-based geographical routing protocol that is capable of finding robust and optimal routes within urban environments. The main principle behind GyTAR is the dynamic and in-sequence selection of intersections through which data packets are forwarded to the destinations. The intersections are chosen considering parameters such as the remaining distance to the destination and the variation in vehicular traffic. Data forwarding between intersections in GyTAR adopts an improved greedy carry-and-forward mechanism. Evaluation of the proposed routing protocol shows significant performance improvement in comparison with other existing routing approaches. With the aid of extensive simulations, we also validate the optimality and sensitivity of significant GyTAR parameters.

A Column Generation Algorithm for Choice-Based Network Revenue Management

Abstract: During the past few years, there has been a trend to enrich traditional revenue management models built upon the independent demand paradigm by accounting for customer choice behavior. This extension involves both modeling and computational challenges. One way to describe choice behavior is to assume that each customer belongs to a segment, which is characterized by a consideration set, i.e., a subset of the products provided by the firm that a customer views as options. Customers choose a particular product according to a multinomial-logit criterion, a model widely used in the marketing literature. In this paper, we consider the choice-based, deterministic, linear programming model (CDLP) of Gallego et al. (2004) [Gallego, G., G. Iyengar, R. Phillips, A. Dubey. 2004. Managing flexible products on a network. Technical Report CORC TR-2004-01, Department of Industrial Engineering and Operations Research, Columbia University, New York], and the follow-up dynamic programming decomposition heuristic of van Ryzin and Liu (2008) [van Ryzin, G. J., Q. Liu. 2008. On the choice-based linear programming model for network revenue management. Manufacturing Service Oper. Management10(2) 288--310]. We focus on the more general version of these models, where customers belong to overlapping segments. To solve the CDLP for real-size networks, we need to develop a column generation algorithm. We prove that the associated column generation subproblem is indeed NP-hard and propose a simple, greedy heuristic to overcome the complexity of an exact algorithm. Our computational results show that the heuristic is quite effective and that the overall approach leads to high-quality, practical solutions.

Submodular maximization with cardinality constraints

Abstract: We consider the problem of maximizing a (non-monotone) submodular function subject to a cardinality constraint. In addition to capturing well-known combinatorial optimization problems, e.g., Max-k-Coverage and Max-Bisection, this problem has applications in other more practical settings such as natural language processing, information retrieval, and machine learning. In this work we present improved approximations for two variants of the cardinality constraint for non-monotone functions. When at most k elements can be chosen, we improve the current best 1/e -- o(1) approximation to a factor that is in the range [1/e + 0.004, 1/2], achieving a tight approximation of 1/2 -- o(1) for k = n/2 and breaking the 1/e barrier for all values of k. When exactly k elements must be chosen, our algorithms improve the current best 1/4 -- o(1) approximation to a factor that is in the range [0.356, 1/2], again achieving a tight approximation of 1/2 -- o(1) for k = n/2. Additionally, some of the algorithms we provide are very fast with time complexities of O(nk), as opposed to previous known algorithms which are continuous in nature, and thus, too slow for applications in the practical settings mentioned above.Our algorithms are based on two new techniques. First, we present a simple randomized greedy approach where in each step a random element is chosen from a set of "reasonably good" elements. This approach might be considered a natural substitute for the greedy algorithm of Nemhauser, Wolsey and Fisher [45], as it retains the same tight guarantee of 1--1/e for monotone objectives and the same time complexity of O(nk), while giving an approximation of 1/e for general non-monotone objectives (while the greedy algorithm of Nemhauser et. al. fails to provide any constant guarantee). Second, we extend the double greedy technique, which achieves a tight 1/2 approximation for unconstrained submodular maximization, to the continuous setting. This allows us to manipulate the natural rates by which elements change, thus bounding the total number of elements chosen.