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Explorable heap selection is the problem of selecting the $n$th smallest value in a binary heap. The key values can only be accessed by traversing through the underlying infinite binary tree, and the complexity of the algorithm is measured…

We focus on the problem of estimating and quantifying uncertainties on the excursion set of a function under a limited evaluation budget. We adopt a Bayesian approach where the objective function is assumed to be a realization of a Gaussian…

The Traveling Salesman Problem (TSP) is one of the most representative NP-hard problems in route planning and a long-standing benchmark in combinatorial optimization. Traditional heuristic tour constructors, such as Farthest or Nearest…

In this paper we study a natural special case of the Traveling Salesman Problem (TSP) with point-locational-uncertainty which we will call the {\em adversarial TSP} problem (ATSP). Given a metric space $(X, d)$ and a set of subsets $R =…

For online matching with the line metric, we present a lower bound of $\Omega(\log n)$ on the approximation ratio of any online (possibly randomized) algorithm. This beats the previous best lower bound of $\Omega(\sqrt{\log n})$ and matches…

The bus-factor is a critical risk indicator that quantifies how many key contributors a project can afford to lose before core knowledge or functionality is compromised. Despite its practical importance, accurately computing the bus-factor…

The paper provides a description of the two recent approximation algorithms for the Asymmetric Traveling Salesman Problem, giving the intuitive description of the works of Feige-Singh[1] and Asadpour et.al\ [2].\newline [1] improves the…

This paper explores a variation of the Traveling Salesperson Problem, where the agent places a circular obstacle next to each node once it visits it. Referred to as the Traveling Salesperson Problem with Circle Placement (TSP-CP), the aim…

We propose a simple subsampling scheme for fast randomized approximate computation of optimal transport distances. This scheme operates on a random subset of the full data and can use any exact algorithm as a black-box back-end, including…

We consider the rooted orienteering problem in Euclidean space: Given $n$ points $P$ in $\mathbb R^d$, a root point $s\in P$ and a budget $\mathcal B>0$, find a path that starts from $s$, has total length at most $\mathcal B$, and visits as…

Surveillance applications require a collection of heterogeneous vehicles to visit a set of targets. In this article, we consider a fundamental routing problem that arises in these applications involving two vehicles. Specifically, we…

In logistic applications that require the pickup and delivery of items, route optimization problems can be modeled as precedence constrained traveling salesperson problems. The combinatorial nature of this problem restricts the application…

We consider a set of Euclidean optimization problems in one dimension, where the cost function associated to the couple of points $x$ and $y$ is the Euclidean distance between them to an arbitrary power $p\ge1$, and the points are chosen at…

The Gap-Hamming-Distance problem arose in the context of proving space lower bounds for a number of key problems in the data stream model. In this problem, Alice and Bob have to decide whether the Hamming distance between their $n$-bit…

We survey results on the hardness of approximating combinatorial optimization problems.

We study approximability of subdense instances of various covering problems on graphs, defined as instances in which the minimum or average degree is Omega(n/psi(n)) for some function psi(n)=omega(1) of the instance size. We design new…

This work presents a tensor-network formulation of the Traveling Salesman Problem (TSP) and several of its variants. The approach represents candidate tours with tensor-network layers, weights them by Boltzmann factors, and enforces…

In recent years, there has been much interest in phase transitions of combinatorial problems. Phase transitions have been successfully used to analyze combinatorial optimization problems, characterize their typical-case features and locate…

When globally optimal solutions of complicated optimization problems cannot be located by evolutionary algorithms (EAs) in polynomial expected running time, the hitting time/running time analysis is not flexible enough to accommodate the…

We propose a combination of a bounding procedure and gradient descent method for solving the Dubins traveling salesman problem, that is, the problem of finding a shortest curvature-constrained tour through a finite number of points in the…