Sharif Digital Repository

We study the problem of maximizing constrained non-monotone submodular functions and provide approximation algorithms that improve existing algorithms in terms of either the approximation factor or simplicity. Different constraints that we study are exact cardinality and multiple knapsack constraints for which we achieve (0.25-)-factor algorithms. We also show, as our main contribution, how to use the continuous greedy process for non-monotone functions and, as a result, obtain a 0.13-factor approximation algorithm for maximization over any solvable down-monotone polytope  

Employing deep learning makes it possible to learn high-level features from raw data, resulting in more precise models. On the other hand, submodularity makes the solution scalable and provides the means to guarantee a lower bound for its performance. In this paper, a deep submodular network (DSN) is introduced, which is a deep network meeting submodularity characteristics. DSN lets modular and submodular features to participate in constructing a tailored model that fits the best with a problem. Various properties of DSN are examined and its learning method is presented. By proving that cost function used for learning process is a convex function, it is concluded that minimization can be... 

We conduct a study on the problem of fair allocation of indivisible goods when maximin share [1] is used as the measure of fairness. Most of the current studies on this notion are limited to the case that the valuations are additive. In this paper, we go beyond additive valuations and consider the cases that the valuations are submodular, fractionally subadditive, and subadditive. We give constant approximation guarantees for agents with submodular and XOS valuations, and a logarithmic bound for the case of agents with subadditive valuations. Furthermore, we complement our results by providing close upper bounds for each class of valuation functions. Finally, we present algorithms to find... 

Abstractive multi-document summarization is a type of automatic text summarization. It obtains information from multiple documents and generates a human-like summary from them. In this paper, we propose an abstractive multi-document summarization method called HMSumm. The proposed method is a combination of extractive and abstractive summarization approaches. First, it constructs an extractive summary from multiple input documents, and then uses it to generate the abstractive summary. Redundant information, which is a global problem in multi-document summarization, is managed in the first step. Specifically, the determinantal point process (DPP) is used to deal with redundancy. This step... 

Submodularity is a discrete domain functional property that can be interpreted as mimicking the role of well-known convexity/concavity properties in the continuous domain. Submodular functions exhibit strong structure that lead to efficient optimization algorithms with provable near-optimality guarantees. These characteristics, namely, efficiency and provable performance bounds, are of particular interest for signal processing (SP) and machine learning (ML) practitioners, as a variety of discrete optimization problems are encountered in a wide range of applications. Conventionally, two general approaches exist to solve discrete problems: 1) relaxation into the continuous domain to obtain an... 

Multiple input multiple output (MIMO) radar is known for its superiority over conventional radar due to its antenna and waveform diversity. Although higher angular resolution, improved parameter identifiability, and better target detection are achieved, the hardware costs (due to multiple transmitters and multiple receivers) and high energy consumption (multiple pulses) limit the usage of MIMO radars in large scale networks. On one hand, higher angle and velocity estimation accuracy is required, but on the other hand, a lower number of antennas/pulses is desirable. To achieve such a compromise, in this work, the Cram'er-Rao lower bound (CRLB) for the angle and velocity estimator is employed... 

Multiple-input multiple-output (MIMO) radar is known for its superiority over conventional radar due to its antenna and waveform diversity. Although higher angular resolution, improved parameter identifiability, and better target detection are achieved, the hardware costs (due to multiple transmitters and multiple receivers) and high-energy consumption (multiple pulses) limit the usage of MIMO radars in large scale networks. On one hand, higher angle and velocity estimation accuracy is required, but on the other hand, a lower number of antennas/pulses is desirable. To achieve such a compromise, in this paper, the Cramér-Rao lower bound (CRLB) for the angle and velocity estimator is employed...