Related papers: Even Faster Knapsack via Rectangular Monotone Min-…
Constrained submodular maximization problems have long been studied, with near-optimal results known under a variety of constraints when the submodular function is monotone. The case of non-monotone submodular maximization is less…
This paper introduces a family of learning-augmented algorithms for online knapsack problems that achieve near Pareto-optimal consistency-robustness trade-offs through a simple combination of trusted learning-augmented and worst-case…
We consider the product knapsack problem, which is the variant of the classical 0-1 knapsack problem where the objective consists of maximizing the product of the profits of the selected items. These profits are allowed to be positive or…
Integer programs with m constraints are solvable in pseudo-polynomial time in $\Delta$, the largest coefficient in a constraint, when m is a fixed constant. We give a new algorithm with a running time of $O(\sqrt{m}\Delta)^{2m} + O(nm)$,…
Robust covariance estimation is the following, well-studied problem in high dimensional statistics: given $N$ samples from a $d$-dimensional Gaussian $\mathcal{N}(\boldsymbol{0}, \Sigma)$, but where an $\varepsilon$-fraction of the samples…
We introduce the first best-of-both-worlds algorithm for contextual combinatorial semi-bandits that simultaneously guarantees $\widetilde{\mathcal{O}}(\sqrt{T})$ regret in the adversarial regime and $\widetilde{\mathcal{O}}(\ln T)$ regret…
Evolutionary algorithms are bio-inspired algorithms that can easily adapt to changing environments. Recent results in the area of runtime analysis have pointed out that algorithms such as the (1+1)~EA and Global SEMO can efficiently…
We study a general online linear optimization problem(OLO). At each round, a subset of objects from a fixed universe of $n$ objects is chosen, and a linear cost associated with the chosen subset is incurred. To measure the performance of…
We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our…
A recent work by [Larsen, SODA 2023] introduced a faster combinatorial alternative to Bansal's SDP algorithm for finding a coloring $x \in \{-1, 1\}^n$ that approximately minimizes the discrepancy $\mathrm{disc}(A, x) := | A x |_{\infty}$…
Many problems are NP-hard and, unless P = NP, do not admit polynomial-time exact algorithms. The fastest known exact algorithms exactly usually take time exponential in the input size. Much research effort has gone into obtaining faster…
We investigate pseudo-polynomial time algorithms for Subset Sum. Given a multi-set $X$ of $n$ positive integers and a target $t$, Subset Sum asks whether some subset of $X$ sums to $t$. Bringmann proposes an $\tilde{O}(n + t)$-time…
In the {\em distributed all-pairs shortest paths} problem (APSP), every node in the weighted undirected distributed network (the CONGEST model) needs to know the distance from every other node using least number of communication rounds…
We study the problem of "isotropically rounding" a polytope $K\subset\mathbb{R}^n$, that is, computing a linear transformation which makes the uniform distribution on the polytope have roughly identity covariance matrix. We assume $K$ is…
We give a new general approach for designing exact exponential-time algorithms for subset problems. In a subset problem the input implicitly describes a family of sets over a universe of size n and the task is to determine whether the…
We consider a multi-armed bandit problem where payoffs are a linear function of an observed stochastic contextual variable. In the scenario where there exists a gap between optimal and suboptimal rewards, several algorithms have been…
Initially developed for the min-knapsack problem, the knapsack cover inequalities are used in the current best relaxations for numerous combinatorial optimization problems of covering type. In spite of their widespread use, these…
One of the most basic graph problems, All-Pairs Shortest Paths (APSP) is known to be solvable in $n^{3-o(1)}$ time, and it is widely open whether it has an $O(n^{3-\epsilon})$ time algorithm for $\epsilon > 0$. To better understand APSP,…
We present improved deterministic algorithms for approximating shortest paths in the Congested Clique model of distributed computing. We obtain $poly(\log\log n)$-round algorithms for the following problems in unweighted undirected…
In this paper, we show that the time complexity of monotone min-plus product of two $n\times n$ matrices is $\tilde{O}(n^{(3+\omega)/2})=\tilde{O}(n^{2.687})$, where $\omega < 2.373$ is the fast matrix multiplication exponent [Alman and…