Greedy algorithm

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

Optimization Algorithms for the Selection of Key Frame Sequences of Variable Length

Abstract: This paper presents a novel optimization-based approach for video key frame selection. We define key frames to be a temporally ordered subsequence of the original video sequence, and the optimal k key frames are the subsequence of length k that optimizes an energy function we define on all subsequences. These optimal key subsequences form a hierarchy, with one such subsequence for every k less than the length of the video n, and this hierarchy can be retrieved all at once using a dynamic programming process with polynomial (O(n3)) computation time. To further reduce computation, an approximate solution based on a greedy algorithm can compute the key frame hierarchy in O(n?log(n)). We also present a hybrid method, which flexibly captures the virtues of both approaches. Our empirical comparisons between the optimal and greedy solutions indicate their results are very close. We show that the greedy algorithm is more appropriate for video streaming and network applications where compression ratios may change dynamically, and provide a method to compute the appropriate times to advance through key frames during video playback of the compressed stream. Additionally, we exploit the results of the greedy algorithm to devise an interactive video content browser. To quantify our algorithms' effectiveness, we propose a new evaluation measure, called "well-distributed" key frames. Our experimental results on several videos show that both the optimal and the greedy algorithms outperform several popular existing algorithms in terms of summarization quality, computational time, and guaranteed convergence.

Multi-target visual tracking with aerial robots

Abstract: We study the problem of tracking mobile targets using a team of aerial robots. Each robot carries a camera to detect targets moving on the ground. The overall goal is to plan for the trajectories of the robots in order to track the most number of targets, and accurately estimate the target locations using the images. The two objectives can conflict since a robot may fly to a higher altitude and potentially cover a larger number of targets at the expense of accuracy. We start by showing that k ≥ 3 robots may not be able to track all n targets while maintaining a constant factor approximation of the optimal quality of tracking at all times. Next, we study the problem of choosing robot trajectories to maximize either the number of targets tracked or the quality of tracking. We formulate this problem as the weighted version of a combinatorial optimization problem known as the Maximum Group Coverage (MGC) problem. A greedy algorithm yields a 1/2 approximation for the weighted MGC problem. Finally, we evaluate the algorithm and the sensing model through simulations and preliminary experiments.

Crossing reduction in circular layouts

Abstract: We propose a two-phase heuristic for crossing reduction in circular layouts. While the first algorithm uses a greedy policy to build a good initial layout, an adaptation of the sifting heuristic for crossing reduction in layered layouts is used for local optimization in the second phase. Both phases are conceptually simpler than previous heuristics, and our extensive experimental results indicate that they also yield fewer crossings. An interesting feature is their straightforward generalization to the weighted case.

Fast Greedy MAP Inference for Determinantal Point Process to Improve Recommendation Diversity

Abstract: The determinantal point process (DPP) is an elegant probabilistic model of repulsion with applications in various machine learning tasks including summarization and search. However, the maximum a posteriori (MAP) inference for DPP which plays an important role in many applications is NP-hard, and even the popular greedy algorithm can still be too computationally expensive to be used in large-scale real-time scenarios. To overcome the computational challenge, in this paper, we propose a novel algorithm to greatly accelerate the greedy MAP inference for DPP. In addition, our algorithm also adapts to scenarios where the repulsion is only required among nearby few items in the result sequence. We apply the proposed algorithm to generate relevant and diverse recommendations. Experimental results show that our proposed algorithm is significantly faster than state-of-the-art competitors, and provides a better relevance-diversity trade-off on several public datasets, which is also confirmed in an online A/B test.

Approximation Algorithms for the Job Interval Selection Problem and Related Scheduling Problems

Abstract: In this paper we consider the job interval selection problem (JISP), a simple scheduling model with a rich history and numerous applications. Special cases of this problem include the so-called real-time scheduling problem (also known as the throughput maximization problem) in single- and multiple-machine environments. In these special cases we have to maximize the number of jobs scheduled between their release date and deadline (preemption is not allowed). Even the single-machine case is NP-hard. The unrelated machines case, as well as other special cases of JISP, are MAX SNP-hard. A simple greedy algorithm gives a two-approximation for JISP. Despite many efforts, this was the best approximation guarantee known, even for throughput maximization on a single machine. In this paper, we break this barrier and show an approximation guarantee of less than 1.582 for arbitrary instances of JISP. For some special cases, we show better results.