Greedy algorithm

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

Off-line compression by greedy textual substitution

Abstract: Greedy off-line textual substitution refers to the following approach to compression or structural inference. Given a long textstring x, a substring w is identified such that replacing all instances of w in x except one by a suitable pair of pointers yields the highest possible contraction of x; the process is then repeated on the contracted textstring until substrings capable of producing contractions can no longer be found. This paper examines computational issues arising in the implementation of this paradigm and describes some applications and experiments.

Monotone Submodular Maximization over a Matroid via Non-Oblivious Local Search

Abstract: We present an optimal, combinatorial $1-1/e$ approximation algorithm for monotone submodular optimization over a matroid constraint. Compared to the continuous greedy algorithm [G. Calinescu et al., IPCO, Springer, Berlin, 2007, pp. 182--196] our algorithm is extremely simple and requires no rounding. It consists of the greedy algorithm followed by a local search. Both phases are run not on the actual objective function, but on a related auxiliary potential function, which is also monotone and submodular. In our previous work on maximum coverage [Y. Filmus and J. Ward, FOCS, IEEE, Piscataway, NJ, 2012, pp. 659--668], the potential function gives more weight to elements covered multiple times. We generalize this approach from coverage functions to arbitrary monotone submodular functions. When the objective function is a coverage function, both definitions of the potential function coincide. Our approach generalizes to the case where the monotone submodular function has restricted curvature. For any curvatu...

SLADE: A Smart Large-Scale Task Decomposer in Crowdsourcing

Abstract: Crowdsourcing has been shown to be effective in a wide range of applications, and is seeing increasing use. A large-scale crowdsourcing task often consists of thousands or millions of atomic tasks, each of which is usually a simple task such as binary choice or simple voting. To distribute a large-scale crowdsourcing task to limited crowd workers, a common practice is to pack a set of atomic tasks into a task bin and send to a crowd worker in a batch. It is challenging to decompose a large-scale crowdsourcing task and execute batches of atomic tasks, which ensures reliable answers at a minimal total cost. Large batches lead to unreliable answers of atomic tasks, while small batches incur unnecessary cost. In this paper, we investigate a general crowdsourcing task decomposition problem, called the S mart L arge-sc A le task DE composer (SLADE) problem, which aims to decompose a large-scale crowdsourcing task to achieve the desired reliability at a minimal cost. We prove the NP-hardness of the SLADE problem and propose solutions in both homogeneous and heterogeneous scenarios. For the homogeneous SLADE problem, where all the atomic tasks share the same reliability requirement, we propose a greedy heuristic algorithm and an efficient and effective approximation framework using an optimal priority queue (OPQ) structure with provable approximation ratio. For the heterogeneous SLADE problem, where the atomic tasks can have different reliability requirements, we extend the OPQ-based framework leveraging a partition strategy, and also prove its approximation guarantee. Finally, we verify the effectiveness and efficiency of the proposed solutions through extensive experiments on representative crowdsourcing platforms.

Algorithms for leader selection in large dynamical networks: Noise-corrupted leaders

Abstract: We examine the leader selection problem in multi-agent dynamical networks where leaders, in addition to relative information from their neighbors, also have access to their own states. We are interested in selecting an a priori specified number of agents as leaders in order to minimize the total variance of the stochastically forced network. Combinatorial nature of this optimal control problem makes computation of the global minimum difficult. We propose a convex relaxation to obtain a lower bound on the global optimal value, and use simple but efficient greedy algorithms to obtain an upper bound. Furthermore, we employ the alternating direction method of multipliers to search for a local minimum. Two examples are provided to illustrate the effectiveness of the developed methods.

A simple polynomial-time rescaling algorithm for solving linear programs

Abstract: The perceptron algorithm, developed mainly in the machine learning literature, is a simple greedy method for finding a feasible solution to a linear program (alternatively, for learning a threshold function. ). In spite of its exponential worst-case complexity, it is often quite useful, in part due to its noise-tolerance and also its overall simplicity. In this paper, we show that a randomized version of the perceptron algorithm with periodic rescaling runs in polynomial-time. The resulting algorithm for linear programming has an elementary description and analysis.