Zhenning Zhang

TL;DR: A local search for the k-means problem with (nonuniform) penalties (k-MPWP) is offered and the above approximation ratio is improved by using multi-swap operation and the sum of penalty cost for each client in P is minimized.

TL;DR: This work introduces a decreasing threshold greedy algorithm with a binary search as its subroutine to solve the problem of maximizing the sum of a monotone non-negative diminishing return submodular (DR-submodular) function and a supermodular function on the integer lattice subject to a cardinality constraint.

TL;DR: This paper offers a local search for the k-MPWP by using single-swap operation and improves the above approximation ratio to \(( 25+ \varepsilon )\) by using multi- Swap operation.

TL;DR: This paper considers the lower-bounded k-median problem (LB k-Median) that extends the classical k- median problem, and aims to open at most k facilities and connect every client to some opened facility, such that the total connection cost is minimized.

TL;DR: A streaming algorithm based on Sieve-Streaming for maximizing a monotone diminishing return submodular (DR-submodular) function with a cardinality constraint on the integer lattice is devised and it is shown to be a one-pass algorithm with approximation ratio.