Greedy algorithm

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

Multi-document Summarization via Budgeted Maximization of Submodular Functions

Abstract: We treat the text summarization problem as maximizing a submodular function under a budget constraint. We show, both theoretically and empirically, a modified greedy algorithm can efficiently solve the budgeted submodular maximization problem near-optimally, and we derive new approximation bounds in doing so. Experiments on DUC'04 task show that our approach is superior to the best-performing method from the DUC'04 evaluation on ROUGE-1 scores.

The Epoch-Greedy algorithm for contextual multi-armed bandits

Abstract: We present Epoch-Greedy, an algorithm for contextual multi-armed bandits (also known as bandits with side information). Epoch-Greedy has the following properties: 1. No knowledge of a time horizon T is necessary. 2. The regret incurred by Epoch-Greedy is controlled by a sample complexity bound for a hypothesis class. 3. The regret scales as O(T2/3S1/3) or better (sometimes, much better). Here S is the complexity term in a sample complexity bound for standard supervised learning.

Submodular meets Spectral: Greedy Algorithms for Subset Selection, Sparse Approximation and Dictionary Selection

Abstract: We study the problem of selecting a subset of k random variables from a large set, in order to obtain the best linear prediction of another variable of interest. This problem can be viewed in the context of both feature selection and sparse approximation. We analyze the performance of widely used greedy heuristics, using insights from the maximization of submodular functions and spectral analysis. We introduce the submodularity ratio as a key quantity to help understand why greedy algorithms perform well even when the variables are highly correlated. Using our techniques, we obtain the strongest known approximation guarantees for this problem, both in terms of the submodularity ratio and the smallest k-sparse eigenvalue of the covariance matrix. We further demonstrate the wide applicability of our techniques by analyzing greedy algorithms for the dictionary selection problem, and significantly improve the previously known guarantees. Our theoretical analysis is complemented by experiments on real-world and synthetic data sets; the experiments show that the submodularity ratio is a stronger predictor of the performance of greedy algorithms than other spectral parameters.

Heuristic algorithms for task assignment in distributed systems

Abstract: Investigate the problem of static task assignment in distributed computing systems, i.e. given a set of k communicating tasks to be executed on a distributed system of n processors, to which processor should each task be assigned? The author proposes a family of heuristic algorithms for Stone's classic model of communicating tasks whose goal is the minimization of the total execution and communication costs incurred by an assignment. In addition, she augments this model to include interference costs which reflect the degree of incompatibility between two tasks. Whereas high communication costs serve as a force of attraction between tasks, causing them to be assigned to the same processor, interference costs serve as a force of repulsion between tasks, causing them to be distributed over many processors. The inclusion of interference costs in the model yields assignments with greater concurrency, thus overcoming the tendency of Stone's model to assign all tasks to one or a few processors. Simulation results show that the algorithms perform well and in particular, that the highly efficient Simple Greedy Algorithm performs almost as well as more complex heuristic algorithms. >

Geographic Routing Using Hyperbolic Space

Abstract: We propose a scalable and reliable point-to-point routing algorithm for ad hoc wireless networks and sensor-nets. Our algorithm assigns to each node of the network a virtual coordinate in the hyperbolic plane, and performs greedy geographic routing with respect to these virtual coordinates. Unlike other proposed greedy routing algorithms based on virtual coordinates, our embedding guarantees that the greedy algorithm is always successful in finding a route to the destination, if such a route exists. We describe a distributed algorithm for computing each node's virtual coordinates in the hyperbolic plane, and for greedily routing packets to a destination point in the hyperbolic plane. (This destination may be the address of another node of the network, or it may be an address associated to a piece of content in a Distributed Hash Table. In the latter case we prove that the greedy routing strategy makes a consistent choice of the node responsible for the address, irrespective of the source address of the request.) We evaluate the resulting algorithm in terms of both path stretch and node congestion.