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The computational equivalence between approximate counting and sampling is well established for polynomial-time algorithms. The most efficient general reduction from counting to sampling is achieved via simulated annealing, where the…
The partition of a problem into smaller sub-problems satisfying certain properties is often a key ingredient in the design of divide-and-conquer algorithms. For questions related to location, the partition problem can be modeled, in…
The knapsack problem is one of the classical problems in combinatorial optimization: Given a set of items, each specified by its size and profit, the goal is to find a maximum profit packing into a knapsack of bounded capacity. In the…
In this paper we apply the multicanonical method of statistical physics on the number-partitioning problem (NPP). This problem is a basic NP-hard problem from computer science, and can be formulated as a spin-glass problem. We compute the…
We investigate the existence of a statistical-computational gap in multiple Gaussian graph alignment. We first generalize a previously established informational threshold from Vassaux and Massouli\'e (2025) to regimes where the number of…
Asadpour, Feige, and Saberi proved that the integrality gap of the configuration LP for the restricted max-min allocation problem is at most $4$. However, their proof does not give a polynomial-time approximation algorithm. A lot of efforts…
Given a matrix $A \in \mathbb{R}^{n\times n}$, we consider the problem of maximizing $x^TAx$ subject to the constraint $x \in \{-1,1\}^n$. This problem, called MaxQP by Charikar and Wirth [FOCS'04], generalizes MaxCut and has natural…
Based on our \bl{\textbf{Random Duality Theory (RDT)}}, in a sequence of our recent papers \cite{Stojnicclupint19,Stojnicclupcmpl19,Stojnicclupplt19}, we introduced a powerful algorithmic mechanism (called \bl{\textbf{CLuP}}) that can be…
We consider an optimal control problem (OCP) for a partial differential equation (PDE) with random coefficients. The optimal control function is a deterministic, distributed forcing term that minimizes an expected quadratic regularized loss…
A long series of recent results and breakthroughs have led to faster and better distributed approximation algorithms for single source shortest paths (SSSP) and related problems in the CONGEST model. The runtime of all these algorithms,…
We initiate the systematic study of a recently introduced polynomial-time analogue of MaxSNP, which includes a large number of well-studied problems (including Nearest and Furthest Neighbor in the Hamming metric, Maximum Inner Product,…
The matching problem between two adjacency matrices can be formulated as the NP-hard quadratic assignment problem (QAP). Previous work on semidefinite programming (SDP) relaxations to the QAP have produced solutions that are often tight in…
The Survivable Network Design problem (SNDP) is a well-studied problem, motivated by the design of networks that are robust to faults under the assumption that any subset of edges up to a specific number can fail. We consider non-uniform…
In this paper, a new graph partitioning problem is introduced. The depth of each part is constrained, i.e., the node count in the longest path of the corresponding sub-graph is no more than a predetermined positive integer value p. An…
We show a relation between quantum learning theory and algorithmic hardness. We use the existence of efficient, local learning algorithms for energy estimation -- such as the classical shadows algorithm -- to prove that finding near-ground…
In the paper, we propose solving optimization problems (OPs) and understanding the Newton method from the optimal control view. We propose a new optimization algorithm based on the optimal control problem (OCP). The algorithm features…
Many engineered systems, such as energy and transportation infrastructures, are networks governed by non-linear physical laws. A primary challenge for operators of these networks is to achieve optimal utilization while maintaining safety…
We consider the dynamic resource allocation problem where the decision space is finite-dimensional, yet the solution must satisfy a large or even infinite number of constraints revealed via streaming data or oracle feedback. We model this…
Distribution Regression on path-space refers to the task of learning functions mapping the law of a stochastic process to a scalar target. The learning procedure based on the notion of path-signature, i.e. a classical transform from rough…
In this paper we consider graph algorithms in models of computation where the space usage (random accessible storage, in addition to the read only input) is sublinear in the number of edges $m$ and the access to input data is constrained.…