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We consider the maximization problem in the value oracle model of functions defined on k-tuples of sets that are submodular in every orthant and r-wise monotone, where k >= 2 and 1
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The course provides a comprehensive overview of digital signal processing theory, covering discrete time, Fourier analysis, filter design, sampling, interpolation and quantization; it also includes a
Adaptive signal processing, A/D and D/A. This module provides the basic
tools for adaptive filtering and a solid mathematical framework for sampling and
quantization
In mathematics, a submodular set function (also known as a submodular function) is a set function whose value, informally, has the property that the difference in the incremental value of the function that a single element makes when added to an input set decreases as the size of the input set increases. Submodular functions have a natural diminishing returns property which makes them suitable for many applications, including approximation algorithms, game theory (as functions modeling user preferences) and electrical networks.
In the mathematical theory of matroids, the rank of a matroid is the maximum size of an independent set in the matroid. The rank of a subset S of elements of the matroid is, similarly, the maximum size of an independent subset of S, and the rank function of the matroid maps sets of elements to their ranks. The rank function is one of the fundamental concepts of matroid theory via which matroids may be axiomatized. Matroid rank functions form an important subclass of the submodular set functions.
Borůvka's algorithm is a greedy algorithm for finding a minimum spanning tree in a graph, or a minimum spanning forest in the case of a graph that is not connected. It was first published in 1926 by Otakar Borůvka as a method of constructing an efficient electricity network for Moravia. The algorithm was rediscovered by Choquet in 1938; again by Florek, Łukasiewicz, Perkal, Steinhaus, and Zubrzycki in 1951; and again by Georges Sollin in 1965. This algorithm is frequently called Sollin's algorithm, especially in the parallel computing literature.
In this thesis, we give new approximation algorithms for some NP-hard problems arising in resource allocation and network design. As a resource allocation problem, we study the Santa Claus problem (also known as the MaxMin Fair Allocation problem) in which ...
Submodular functions are a widely studied topic in theoretical computer science. They have found several applications both theoretical and practical in the fields of economics, combinatorial optimization and machine learning. More recently, there have also ...
This letter studies the problem of minimizing increasing set functions, equivalently, maximizing decreasing set functions, over the base matroid. This setting has received great interest, since it generalizes several applied problems including actuator and ...
