Related papers: An O(log k log^2 n)-competitive Randomized Algorit…

Many signal processing problems can be solved by maximizing the fitness of a segmented model over all possible partitions of the data interval. This letter describes a simple but powerful algorithm that searches the exponentially large…

We consider the problem of constructing codes that can correct deletions that are localized within a certain part of the codeword that is unknown a priori. Namely, the model that we study is when at most $k$ deletions occur in a window of…

We study the problem of multiway number partition optimization, which has a myriad of applications in the decision, learning and optimization literature. Even though the original multiway partitioning problem is NP-hard and requires…

We propose and develop an efficient implementation of the robust tabu search heuristic for sparse quadratic assignment problems. The traditional implementation of the heuristic applicable to all quadratic assignment problems is of O(N^2)…

We study the $k$-server problem in the resource augmentation setting i.e., when the performance of the online algorithm with $k$ servers is compared to the offline optimal solution with $h \leq k$ servers. The problem is very poorly…

Knapsack is one of the most fundamental problems in theoretical computer science. In the $(1 - \epsilon)$-approximation setting, although there is a fine-grained lower bound of $(n + 1 / \epsilon) ^ {2 - o(1)}$ based on the $(\min,…

We present an $O(n\sqrt{\log n})$ time and linear space algorithm for sorting real numbers. This breaks the long time illusion that real numbers have to be sorted by comparison sorting and take $\Omega (n\log n)$ time to be sorted.

The logarithm-determinant is an widely-present operation in many areas of physics and computer science. Derivatives of the logarithm-determinant compute physically relevant quantities in statistical physics models, quantum field theories,…

We present semi-streaming algorithms for basic graph problems that have optimal per-edge processing times and therefore surpass all previous semi-streaming algorithms for these tasks. The semi-streaming model, which is appropriate when…

We propose faster algorithms for the following three optimization problems on $n$ collinear points, i.e., points in dimension one. The first two problems are known to be NP-hard in higher dimensions. 1- Maximizing total area of disjoint…

We give a polynomial-time algorithm for OnlineSetCover with a competitive ratio of $O(\log mn)$ when the elements are revealed in random order, essentially matching the best possible offline bound of $O(\log n)$ and circumventing the…

Given a reference set $R$ of $n$ points and a query set $Q$ of $m$ points in a metric space, this paper studies an important problem of finding $k$-nearest neighbors of every point $q \in Q$ in the set $R$ in a near-linear time. In the…

We present randomized algorithms for some well-studied, hard combinatorial problems: the k-path problem, the p-packing of q-sets problem, and the q-dimensional p-matching problem. Our algorithms solve these problems with high probability in…

Several algorithms with an approximation guarantee of $O(\log n)$ are known for the Set Cover problem, where $n$ is the number of elements. We study a generalization of the Set Cover problem, called the Partition Set Cover problem. Here,…

This article introduces a new optimization method to improve mergesort's runtime complexity, when sorting sequences that have equal keys to $O(n log_2 k)$, where $k$ is the number of distinct keys in the sequence. When $k$ is constant, it…

In the streaming model, the order of the stream can significantly affect the difficulty of a problem. A $t$-semirandom stream was introduced as an interpolation between random-order ($t=1$) and adversarial-order ($t=n$) streams where an…

We prove that the Sinkhorn algorithm converges at a rate of $O(k^{-1} \log k)$ in $\ell_1$-norm marginal error, in the asymptotically scalable case. This almost closes the gap between the lower bound $\Omega(k^{-1})$ (Qu et al., 2025) and…

We present a new approach to the minimum-cost integral flow problem for small values of the flow. It reduces the problem to the tests of simple multi-variate polynomials over a finite field of characteristic two for non-identity with zero.…

The k-median problem is a well-known strongly NP-hard combinatorial optimization problem of both theoretical and practical significance. The previous best approximation ratio for this problem is 2.611+\epsilon (Bryka et al. 2014) based on…

In the Orthogonal Vectors problem (OV), we are given two families $A, B$ of subsets of $\{1,\ldots,d\}$, each of size $n$, and the task is to decide whether there exists a pair $a \in A$ and $b \in B$ such that $a \cap b = \emptyset$.…