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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 which given demands for the items must be satisfied. Ordering a set of items incurs a cost according to a set function, with properties depending on the problem under consideration. Demand for an item at time $t$ can be satisfied by an order on any day prior to $t$, but a holding cost is charged for storing the items during the intermediate period; the goal is to minimize the sum of the ordering and holding cost. Our approximation factor for both problems is $O(log log min(N,T))$; this improves exponentially on the previous best results.
In the relay placement problem the input is a set of sensors and a number $r ge 1$, the communication range of a relay. In the one-tier version of the problem the objective is to place a minimum number of relays so that between every pair of sensors
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 consider the $k$-clustering problem with $ell_p$-norm cost, which includes $k$-median, $k$-means and $k$-center cost functions, under an individual notion of fairness proposed by Jung et al. [2020]: given a set of points $P$ of size $n$, a set of
In the Priority Steiner Tree (PST) problem, we are given an undirected graph $G=(V,E)$ with a source $s in V$ and terminals $T subseteq V setminus {s}$, where each terminal $v in T$ requires a nonnegative priority $P(v)$. The goal is to compute a min
In this paper, we consider several finite-horizon Bayesian multi-armed bandit problems with side constraints which are computationally intractable (NP-Hard) and for which no optimal (or near optimal) algorithms are known to exist with sub-exponential