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We revisit the traveling salesman problem with neighborhoods (TSPN) and propose several new approximation algorithms. These constitute either first approximations (for hyperplanes, lines, and balls in $\mathbb{R}^d$, for $d\geq 3$) or…
In the weighted flow-time problem on a single machine, we are given a set of n jobs, where each job has a processing requirement p_j, release date r_j and weight w_j. The goal is to find a preemptive schedule which minimizes the sum of…
We consider a general class of binary packing problems with a convex quadratic knapsack constraint. We prove that these problems are APX-hard to approximate and present constant-factor approximation algorithms based upon three different…
We present new approximation schemes for bin packing based on the following two approaches: (1) partitioning the given problem into mostly identical sub-problems of constant size and then construct a solution by combining the solutions of…
Low cost Unmanned Aerial Vehicles (UAVs) need multiple refuels to accomplish large area coverage. The number of refueling stations and their placement plays a vital role in determining coverage efficiency. In this paper, we propose the use…
In this paper, we study the problem of coverage planning by a mobile robot with a limited energy budget. The objective of the robot is to cover every point in the environment while minimizing the traveled path length. The environment is…
Given a set S of integers whose sum is zero, consider the problem of finding a permutation of these integers such that: (i) all prefix sums of the ordering are nonnegative, and (ii) the maximum value of a prefix sum is minimized. Kellerer…
The Capacitated Location Routing Problem is an important planning and routing problem in logistics, which generalizes the capacitated vehicle routing problem and the uncapacitated facility location problem. In this problem, we are given a…
In 1982, Drezner proposed the (1|1)-centroid problem on the plane, in which two players, called the leader and the follower, open facilities to provide service to customers in a competitive manner. The leader opens the first facility, and…
Given a graph, the general problem to cover the maximum number of vertices by a collection of vertex-disjoint long paths seemingly escapes from the literature. A path containing at least $k$ vertices is considered long. When $k \le 3$, the…
We study the labeled multi-robot path planning problem in continuous 2D and 3D domains in the absence of obstacles where robots must not collide with each other. For an arbitrary number of robots in arbitrary initial and goal arrangements,…
The problem of finding the shortest path for a vehicle visiting a given sequence of target points subject to the motion constraints of the vehicle is an important problem that arises in several monitoring and surveillance applications…
This paper addresses the challenging scheduling problem of coflows with release times, with the objective of minimizing the total weighted completion time. Previous literature has predominantly concentrated on establishing the scheduling…
The Gromov-Wasserstein distance is a notable extension of optimal transport. In contrast to the classic Wasserstein distance, it solves a quadratic assignment problem that minimizes the pair-wise distance distortion under the transportation…
We give new approximation algorithms for the submodular joint replenishment problem and the inventory routing problem, using an iterative rounding approach. In both problems, we are given a set of $N$ items and a discrete time horizon of…
We study a two-dimensional generalization of the classical Bin Packing problem, denoted as 2D Demand Bin Packing. In this context, each bin is a horizontal timeline, and rectangular tasks (representing electric appliances or computational…
In the past decade, many parameterized algorithms were developed for packing problems. Our goal is to obtain tradeoffs that improve the running times of these algorithms at the cost of computing approximate solutions. Consider a packing…
We study an extension of the classical Bin Packing Problem, where each item consumes the bin capacity during a given time window that depends on the item itself. The problem asks for finding the minimum number of bins to pack all the items…
We consider the precedence-constrained scheduling problem to minimize the total weighted completion time. For a single machine several $2$-approximation algorithms are known, which are based on linear programming and network flows. We show…
Low-thrust trajectory design relies heavily on repeated evaluations of fuel consumption and transfer feasibility, which require expensive optimal control solutions. In this work, we show these quantities can be accurately approximated by…