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Given a metric $(V,d)$ and a $textsf{root} in V$, the classic $textsf{$k$-TSP}$ problem is to find a tour originating at the $textsf{root}$ of minimum length that visits at least $k$ nodes in $V$. In this work, motivated by applications where the input to an optimization problem is uncertain, we study two stochast
Robust optimization is a widely studied area in operations research, where the algorithm takes as input a range of values and outputs a single solution that performs well for the entire range. Specifically, a robust algorithm aims to minimize regret,
We consider the problem of designing sublinear time algorithms for estimating the cost of a minimum metric traveling salesman (TSP) tour. Specifically, given access to a $n times n$ distance matrix $D$ that specifies pairwise distances between $n$ po
In the submodular cover problem, we are given a non-negative monotone submodular function $f$ over a ground set $E$ of items, and the goal is to choose a smallest subset $S subseteq E$ such that $f(S) = Q$ where $Q = f(E)$. In the stochastic version
The general adwords problem has remained largely unresolved. We define a subcase called {em $k$-TYPICAL}, $k in Zplus$, as follows: the total budget of all the bidders is sufficient to buy $k$ bids for each bidder. This seems a reasonable assumption
A string $S[1,n]$ is a power (or tandem repeat) of order $k$ and period $n/k$ if it can decomposed into $k$ consecutive equal-length blocks of letters. Powers and periods are fundamental to string processing, and algorithms for their efficient comput