We study the correlated stochastic knapsack problem of a submodular target function, with optional additional constraints. We utilize the multilinear extension of submodular function, and bundle it with an adaptation of the relaxed linear constraints from Ma [Mathematics of Operations Research, Volume 43(3), 2018] on correlated stochastic knapsack problem. The relaxation is then solved by the stochastic continuous greedy algorithm, and rounded by a novel method to fit the contention resolution scheme (Feldman et al. [FOCS 2011]). We obtain a pseudo-polynomial time $(1 - 1/\sqrt{e})/2 \simeq 0.1967$ approximation algorithm with or without those additional constraints, eliminating the need of a key assumption and improving on the $(1 - 1/\sqrt[4]{e})/2 \simeq 0.1106$ approximation by Fukunaga et al. [AAAI 2019].

The coflow scheduling problem has emerged as a popular abstraction in the last few years to study data communication problems within a data center[6]. In this basic framework, each coflow has a set of communication demands and the goal is to schedule many coflows in a manner that minimizes the total weighted completion time. A coflow is said to complete when all its communication needs are met. This problem has been extremely well studied for the case of complete bipartite graphs that model a data center with full bisection bandwidth and several approximation algorithms and effective heuristics have been proposed recently[1,2,29]. In this work, we study a slightly different model of coflow scheduling in general graphs (to capture traffic between data centers [15,29]) and develop practical and efficient approximation algorithms for it. Our main result is a randomized 2 approximation algorithm for the single path and free path model, significantly improving prior work. In addition, we demonstrate via extensive experiments that the algorithm is practical, easy to implement and performs well in practice.

In this paper we consider the classical Connected Dominating Set (CDS) problem. Twenty years ago, Guha and Khuller developed two algorithms for this problem - a centralized greedy approach with an approximation guarantee of H(D) +2, and a local greedy approach with an approximation guarantee of 2(H(D)+1) (where H() is the harmonic function, and D is the maximum degree in the graph). A local greedy algorithm uses significantly less information about the graph, and can be useful in a variety of contexts. However, a fundamental question remained - can we get a local greedy algorithm with the same performance guarantee as the global greedy algorithm without the penalty of the multiplicative factor of "2" in the approximation factor? In this paper, we answer that question in the affirmative.