Clustering is a classic topic in optimization with k-means being one of the most fundamental such problems. In the absence of any restrictions on the input, the best-known algorithm for k-means in Euclidean space with a provable guarantee is a simple local ...
We design new approximation algorithms for the problems of optimizing submodular and supermodular functions subject to a single matroid constraint. Specifically, we consider the case in which we wish to maximize a monotone increasing submodular function or ...
We consider the classical k-means clustering problem in the setting of bi-criteria approximation, in which an algorithm is allowed to output beta*k > k clusters, and must produce a clustering with cost at most alpha times the to the cost of the optimal set ...
Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik2016
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
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. A lot of recent effort has been devoted to developing distributed algo ...
In a stochastic probing problem we are given a universe E, and a probability that each element e in E is active. We determine if an element is active by probing it, and whenever a probed element is active, we must permanently include it in our solution. Mo ...
