Related papers: The Complete Vertex p-Center Problem
The facility location problems (FLPs) are a typical class of NP-hard combinatorial optimization problems, which are widely seen in the supply chain and logistics. Many mathematical and heuristic algorithms have been developed for optimizing…
This paper primarily focuses on figuring out the best array of cameras, or visual sensors, so that such a placement enables the maximum utilization of these visual sensors. Maximizing the utilization of these cameras can convert to another…
The problem of covering random points in a plane with sets of a given shape has several practical applications in communications and operations research. One especially prominent application is the coverage of randomly-located points of…
Ready Mixed Concrete Delivery Problem (RMCDP) is a multi-objective multi-constraint dynamic combinatorial optimization problem. From the operational research prospective, it is a real life logistic problem that is hard to be solved with…
The problem of coverage control, i.e., of coordinating multiple agents to optimally cover an area, arises in various applications. However, coverage applications face two major challenges: (1) dealing with nonlinear dynamics while…
We consider the set multi-cover problem in geometric settings. Given a set of points P and a collection of geometric shapes (or sets) F, we wish to find a minimum cardinality subset of F such that each point p in P is covered by (contained…
In this paper we give the first efficient algorithms for the $k$-center problem on dynamic graphs undergoing edge updates. In this problem, the goal is to partition the input into $k$ sets by choosing $k$ centers such that the maximum…
The Covering Salesman Problem (CSP) is a generalization of the Traveling Salesman Problem in which the tour is not required to visit all vertices, as long as all vertices are covered by the tour. The objective of CSP is to find a minimum…
The goal in the stochastic vertex cover problem is to obtain an approximately minimum vertex cover for a graph $G^\star$ that is realized by sampling each edge independently with some probability $p\in (0, 1]$ in a base graph $G = (V, E)$.…
We consider single-machine scheduling problems that are natural generalizations or variations of the min-sum set cover problem and the min-sum vertex cover problem. For each of these problems, we give new approximation algorithms. Some of…
This paper presents a new model for solving the optimal server location problem in a spatial hypercube queueing model. Unlike deterministic location models, our approach accounts for server availability, varying utilization levels, and…
Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…
Given a set of disks in the plane, the goal of the problem studied in this paper is to choose a subset of these disks such that none of its members contains the centre of any other. Each disk not in this subset must be merged with one of…
We consider the problem of computing the Fr\'echet distance between two curves for which the exact locations of the vertices are unknown. Each vertex may be placed in a given uncertainty region for that vertex, and the objective is to place…
As massive graphs become more prevalent, there is a rapidly growing need for scalable algorithms that solve classical graph problems, such as maximum matching and minimum vertex cover, on large datasets. For massive inputs, several…
The VertexCover problem is proven to be computationally hard in different ways: It is NP-complete to find an optimal solution and even NP-hard to find an approximation with reasonable factors. In contrast, recent experiments suggest that on…
In this paper, we present approximation algorithms for combinatorial optimization problems under probabilistic constraints. Specifically, we focus on stochastic variants of two important combinatorial optimization problems: the k-center…
A variant of the well-known Set Covering Problem is studied in this paper, where subsets of a collection have to be selected, and pairwise conflicts among subsets of items exist. The selection of each subset has a cost, and the inclusion of…
We introduce a class of budgeted prize-collecting covering subgraph problems. For an input graph with prizes on the vertices and costs on the edges, the aim of these problems is to find a connected subgraph such that the cost of its edges…
Linear programming has played a key role in the study of algorithms for combinatorial optimization problems. In the field of approximation algorithms, this is well illustrated by the uncapacitated facility location problem. A variety of…