Greedy algorithm

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

Design of an effective algorithm for fast response to the re-scheduling of railway traffic during disturbances

Abstract: An attractive and sustainable railway traffic system is characterized by having a high security, high accessibility, high energy performance and offering reliable services with sufficient punctuality. At the same time, the network is to be utilized to a large extent in a cost-effective way. This requires a continuous balance between maintaining a high utilization and sufficiently high robustness to minimize the sensitivity to disturbances. The occurrence of some disturbances can be prevented to some extent but the occurrence of unpredictable events are unavoidable and their consequences then need to be analyzed, minimized and communicated to the affected users. Valuable information necessary to perform a complete consequence analysis of a disturbance and the re-scheduling is however not always available for the traffic managers. With current conditions, it is also not always possible for the traffic managers to take this information into account since he or she needs to act fast without any decision-support assisting in computing an effective re-scheduling solution. In previous research we have designed an optimization-based approach for re-scheduling which seems promising. However, for certain scenarios it is difficult to find good solutions within seconds. Therefore, we have developed a greedy algorithm which effectively delivers good solutions within the permitted time as a complement to the previous approach. To quickly retrieve a feasible solution the algorithm performs a depth-first search using an evaluation function to prioritise when conflicts arise and then branches according to a set of criteria.

From the Information Bottleneck to the Privacy Funnel

Abstract: We focus on the disclosure-privacy trade-off encountered by users who wish to disclose some information to an analyst, that is correlated with their private data, in the hope of receiving some utility. To preserve privacy, user data is transformed before it is disclosed, according to a probabilistic privacy mapping. We formalize the disclosure-collateral setting, and provide a single letter characterization of the trade-off between disclosure and privacy. We then formulate the design of the privacy mapping as the Privacy Funnel optimization. This optimization problem being non-convex, we leverage connections to the information bottleneck method, to provide a greedy algorithm, and an alternating iteration algorithm, that are locally optimal, and that we evaluate on synthetic data. We then turn our attention to the case Gaussian user data, and provide a closedform privacy mapping that is optimal in the class of Gaussian mappings. Finally, we show how the Privacy Funnel relates to other privacy-utility frameworks, and justify the generality of the log-loss as an inference cost function for private data.

Fast Greedy Algorithms in MapReduce and Streaming

Abstract: Greedy algorithms are practitioners’ best friends—they are intuitive, are simple to implement, and often lead to very good solutions. However, implementing greedy algorithms in a distributed setting is challenging since the greedy choice is inherently sequential, and it is not clear how to take advantage of the extra processing power. Our main result is a powerful sampling technique that aids in parallelization of sequential algorithms. Armed with this primitive, we then adapt a broad class of greedy algorithms to the MapReduce paradigm; this class includes maximum cover and submodular maximization subject to p-system constraint problems. Our method yields efficient algorithms that run in a logarithmic number of rounds while obtaining solutions that are arbitrarily close to those produced by the standard sequential greedy algorithm. We begin with algorithms for modular maximization subject to a matroid constraint and then extend this approach to obtain approximation algorithms for submodular maximization subject to knapsack or p-system constraints.

Task clustering and scheduling for distributed memory parallel architectures

Abstract: This paper addresses the problem of scheduling parallel programs represented as directed acyclic task graphs for execution on distributed memory parallel architectures. Because of the high communication overhead in existing parallel machines, a crucial step in scheduling is task clustering, the process of coalescing fine grain tasks into single coarser ones so that the overall execution time is minimized. The task clustering problem is NP-hard, even when the number of processors is unbounded and task duplication is allowed. A simple greedy algorithm is presented for this problem which, for a task graph with arbitrary granularity, produces a schedule whose makespan is at most twice optimal. Indeed, the quality of the schedule improves as the granularity of the task graph becomes larger. For example, if the granularity is at least 1/2, the makespan of the schedule is at most 5/3 times optimal. For a task graph with n tasks and e inter-task communication constraints, the algorithm runs in O(n(n lg n+e)) time, which is n times faster than the currently best known algorithm for this problem. Similar algorithms are developed that produce: (1) optimal schedules for coarse grain graphs; (2) 2-optimal schedules for trees with no task duplication; and (3) optimal schedules for coarse grain trees with no task duplication.