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We consider communication problems in the setting of mobile agents deployed in an edge-weighted network. The assumption of the paper is that each agent has some energy that it can transfer to any other agent when they meet (together with the information it holds). The paper deals with three communication problems: data delivery,convergecast and broadcast. These problems are posed for a centralized scheduler which has full knowledge of the instance. It is already known that, without energy exchange, all three problems are NP-complete even if the network is a line. Surprisingly, if we allow the agents to exchange energy, we show that all three problems are polynomially solvable on trees and have linear time algorithms on the line. On the other hand for general undirected and directed graphs we show that these problems, even if energy exchange is allowed, are still NP-complete.
This paper presents universal algorithms for clustering problems, including the widely studied $k$-median, $k$-means, and $k$-center objectives. The input is a metric space containing all potential client locations. The algorithm must select $k$ clus
We consider the problem of finding textit{semi-matching} in bipartite graphs which is also extensively studied under various names in the scheduling literature. We give faster algorithms for both weighted and unweighted case. For the weighted case,
Covering problems are fundamental classical problems in optimization, computer science and complexity theory. Typically an input to these problems is a family of sets over a finite universe and the goal is to cover the elements of the universe with a
The restless bandit problem is one of the most well-studied generalizations of the celebrated stochastic multi-armed bandit problem in decision theory. In its ultimate generality, the restless bandit problem is known to be PSPACE-Hard to approximate
We give new approximation algorithms for the submodular joint replenishment problem and the inventory routing problem, using an iterative rounding approach. In both problems, we are given a set of $N$ items and a discrete time horizon of $T$ days in