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We introduce a graph partitioning problem motivated by computational topology and propose two algorithms that produce approximate solutions. Specifically, given a weighted, undirected graph $G$ and a positive integer $k$, we desire to find…
A tree $\sigma$-spanner of a positively real-weighted $n$-vertex and $m$-edge undirected graph $G$ is a spanning tree $T$ of $G$ which approximately preserves (i.e., up to a multiplicative stretch factor $\sigma$) distances in $G$. Tree…
The traveling salesman problem is a fundamental combinatorial optimization problem with strong exact algorithms. However, as problems scale up, these exact algorithms fail to provide a solution in a reasonable time. To resolve this, current…
Sequential Convex Programming (SCP) has recently gained popularity as a tool for trajectory optimization due to its sound theoretical properties and practical performance. Yet, most SCP-based methods for trajectory optimization are…
The travelling salesman problem (TSP) is a popular NP-hard-combinatorial optimization problem that requires finding the optimal way for a salesman to travel through different cities once and return to the initial city. The existing methods…
Autonomous robotic inspection, where a robot moves through its environment and inspects points of interest, has applications in industrial settings, structural health monitoring, and medicine. Planning the paths for a robot to safely and…
There are emerging transportation problems known as the Traveling Salesman Problem with Drone (TSPD) and the Flying Sidekick Traveling Salesman Problem (FSTSP) that involve using a drone in conjunction with a truck for package delivery.…
In the maximum traveling salesman problem (Max TSP) we are given a complete undirected graph with nonnegative weights on the edges and we wish to compute a traveling salesman tour of maximum weight. We present a fast combinatorial $\frac…
Optimizing delivery routes for last-mile logistics service is challenging and has attracted the attention of many researchers. These problems are usually modeled and solved as variants of vehicle routing problems (VRPs) with challenging…
We consider the following natural "above guarantee" parameterization of the classical Longest Path problem: For given vertices s and t of a graph G, and an integer k, the problem Longest Detour asks for an (s,t)-path in G that is at least k…
Graph neural networks are useful for learning problems, as well as for combinatorial and graph problems such as the Subgraph Isomorphism Problem and the Traveling Salesman Problem. We describe an approach for computing Steiner Trees by…
The travelling salesperson problem (TSP) is a classic resource allocation problem used to find an optimal order of doing a set of tasks while minimizing (or maximizing) an associated objective function. It is widely used in robotics for…
We study the fair capacitated vehicle routing problem, in which a fleet of vehicles must serve a set of customers such that the difference between the longest and shortest route, the range, is minimized. A key challenge is that the range…
In this thesis, we present new techniques to deal with fundamental algorithmic graph problems where graphs are directed and partially dynamic, i.e. undergo either a sequence of edge insertions or deletions: - Single-Source Reachability…
We examine the problem of maximizing the reachability of a given source in temporal graphs that are given as the union of k temporal paths, i.e., every given path is a sequence of edges with strictly increasing labels that denote…
This paper presents a framework to tackle combinatorial optimization problems using neural networks and reinforcement learning. We focus on the traveling salesman problem (TSP) and train a recurrent network that, given a set of city…
In this paper, we look at the problem of finding the tour of maximum reward on an undirected graph where the reward is a submodular function, that has a curvature of $\kappa$, of the edges in the tour. This problem is known to be NP-hard.…
In the new wave of artificial intelligence, deep learning is impacting various industries. As a closely related area, optimization algorithms greatly contribute to the development of deep learning. But the reverse applications are still…
The graph parameters highway dimension and skeleton dimension were introduced to capture the properties of transportation networks. As many important optimization problems like Travelling Salesperson, Steiner Tree or $k$-Center arise in…
We consider the fundamental problem of sampling the optimal transport coupling between given source and target distributions. In certain cases, the optimal transport plan takes the form of a one-to-one mapping from the source support to the…