Open AccessProceedings Article
Submodular Optimization with Submodular Cover and Submodular Knapsack Constraints
Rishabh Iyer,Jeff A. Bilmes +1 more
- Vol. 26, pp 2436-2444
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TLDR
It is shown that both these problems are closely related and an approximation algorithm solving one can be used to obtain an approximation guarantee for the other, and hardness results for both problems are provided, thus showing that the approximation factors are tight up to log-factors.Abstract:
We investigate two new optimization problems — minimizing a submodular function subject to a submodular lower bound constraint (submodular cover) and maximizing a submodular function subject to a submodular upper bound constraint (submodular knapsack). We are motivated by a number of real-world applications in machine learning including sensor placement and data subset selection, which require maximizing a certain submodular function (like coverage or diversity) while simultaneously minimizing another (like cooperative cost). These problems are often posed as minimizing the difference between submodular functions [9, 25] which is in the worst case inapproximable. We show, however, that by phrasing these problems as constrained optimization, which is more natural for many applications, we achieve a number of bounded approximation guarantees. We also show that both these problems are closely related and an approximation algorithm solving one can be used to obtain an approximation guarantee for the other. We provide hardness results for both problems thus showing that our approximation factors are tight up to log-factors. Finally, we empirically demonstrate the performance and good scalability properties of our algorithms.read more
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References
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Book
Approximation Algorithms
TL;DR: Covering the basic techniques used in the latest research work, the author consolidates progress made so far, including some very recent and promising results, and conveys the beauty and excitement of work in the field.
Proceedings ArticleDOI
Interactive graph cuts for optimal boundary & region segmentation of objects in N-D images
Yuri Boykov,Marie-Pierre Jolly +1 more
TL;DR: In this paper, the user marks certain pixels as "object" or "background" to provide hard constraints for segmentation, and additional soft constraints incorporate both boundary and region information.
Journal ArticleDOI
A threshold of ln n for approximating set cover
TL;DR: It is proved that (1 - o(1) ln n setcover is a threshold below which setcover cannot be approximated efficiently, unless NP has slightlysuperpolynomial time algorithms.
Darpa Timit Acoustic-Phonetic Continuous Speech Corpus CD-ROM {TIMIT} | NIST
John S. Garofolo,Lori Lamel,W M. Fisher,Jonathan G. Fiscus,David S. Pallett,Nancy L. Dahlgren +5 more
Dataset
TIMIT Acoustic-Phonetic Continuous Speech Corpus
John S. Garofolo,Lori Lamel,William M. Fisher,Jonathan C. Fiscus,David S. Pallett,Nancy L. Dahlgren,Victor W. Zue +6 more
TL;DR: The TIMIT corpus as mentioned in this paper contains broadband recordings of 630 speakers of eight major dialects of American English, each reading ten phonetically rich sentences, including time-aligned orthographic, phonetic and word transcriptions as well as a 16-bit, 16kHz speech waveform file for each utterance.