Related papers: Multimodal Search on a Line

This paper is concerned with determining the shortest path for a pursuer aiming to intercept a moving target travelling at a constant speed. To address this challenge, we introduce an efficient mathematical model outlined as an optimal…

We consider the problem of finding a door along a wall with a blind robot that neither knows the distance to the door nor the direction towards of the door. This problem can be solved with the well-known doubling strategy yielding an…

We study the online traveling repairperson problem on a line within the recently proposed learning-augmented framework, which provides predictions on the requests to be served via machine learning. In the original model (with no…

We consider a search problem on a $2$-dimensional infinite grid with a single mobile agent. The goal of the agent is to find her way home, which is located in a grid cell chosen by an adversary. Initially, the agent is provided with an…

Approximate nearest-neighbor search is a fundamental algorithmic problem that continues to inspire study due its essential role in numerous contexts. In contrast to most prior work, which has focused on point sets, we consider…

In this paper, we tackle the Multiple Watchman Route Problem (MWRP), which aims to find a set of paths that M watchmen can follow such that every location on the map can be seen by at least one watchman. First, we propose multiple methods…

We provide a simple method and relevant theoretical analysis for efficiently estimating higher-order lp distances. While the analysis mainly focuses on l4, our methodology extends naturally to p = 6,8,10..., (i.e., when p is even).…

In multi-agent search planning for a randomly moving and camouflaging target, we examine heterogeneous searchers that differ in terms of their endurance level, travel speed, and detection ability. This leads to a convex mixed-integer…

Constrained Optimum Path (COP) problems appear in many real-life applications, especially on communication networks. Some of these problems have been considered and solved by specific techniques which are usually difficult to extend. In…

In this extended abstract, we report on ongoing work towards an approximate multimodal optimization algorithm with asymptotic guarantees. Multimodal optimization is the problem of finding all local optimal solutions (modes) to a path…

Searching for a line on the plane with $n$ unit speed robots is a classic online problem that dates back to the 50's, and for which competitive ratio upper bounds are known for every $n\geq 1$. In this work we improve the best lower bound…

In this paper, we study the symmetric rendezvous search problem on the line with n > 2 robots that are unaware of their locations and the initial distances between them. In the symmetric version of this problem, the robots execute the same…

Multi-task learning is a powerful method for solving several tasks jointly by learning robust representation. Optimization of the multi-task learning model is a more complex task than a single-task due to task conflict. Based on theoretical…

We study a variant of the competitive facility location problem, in which a company is to locate new facilities in a market where competitor's facilities already exist. We consider the scenario where only a limited number of possible…

The problem of mobile position estimation in multipath scenarios is addressed. A low-complexity, fully-adaptive algorithm is proposed, based on the pseudo maximum likelihood approach. The processing is done exclusively on-board at the…

We consider machine learning in a comparison-based setting where we are given a set of points in a metric space, but we have no access to the actual distances between the points. Instead, we can only ask an oracle whether the distance…

We study the rectilinear Marco Polo problem, which generalizes the Euclidean version of the Marco Polo problem for performing geometric localization to rectilinear search environments, such as in geometries motivated from urban settings,…

We consider the open, non-preemptive online Dial-a-Ride problem on the real line, where transportation requests appear over time and need to be served by a single server. We give a lower bound of 2.0585 on the competitive ratio, which is…

This paper proposes a nonmonotone proximal quasi-Newton algorithm for unconstrained convex multiobjective composite optimization problems. To design the search direction, we minimize the max-scalarization of the variations of the Hessian…

We consider a perimeter defense problem in a planar conical environment in which a single vehicle, having a finite capture radius, aims to defend a concentric perimeter from mobile intruders. The intruders are arbitrarily released at the…