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We consider the fundamental problem of allocating $T$ indivisible items that arrive over time to $n$ agents with additive preferences, with the goal of minimizing envy. This problem is tightly connected to online multicolor discrepancy:…
We consider a vehicle routing problem which seeks to minimize cost subject to service level constraints on several groups of deliveries. This problem captures some essential challenges faced by a logistics provider which operates…
We address the Diverse Traveling Salesman Problem (D-TSP), a bi-criteria optimization challenge that seeks a set of $k$ distinct TSP tours. The objective requires every selected tour to have a length at most $c|T^*|$ (where $|T^*|$ is the…
Given an integer dimension K and a simple, undirected graph G with positive edge weights, the Distance Geometry Problem (DGP) aims to find a realization function mapping each vertex to a coordinate in K-dimensional space such that the…
We consider facility location problems with a new form of equity criterion. Demand points have preference order on the sites where the plants can be located. The goal is to find the location of the facilities minimizing the envy felt by the…
The vertex connectivity of a graph $G$ is the size of the smallest set of vertices $S$ such that $G \setminus S$ is disconnected. For the class of planar graphs, the problem of vertex connectivity is well-studied, both from structural and…
A long line of literature has focused on the problem of selecting a team of individuals from a large pool of candidates, such that certain constraints are respected, and a given objective function is maximized. Even though extant research…
A highly successful approach to route planning in networks (particularly road networks) is to identify a hierarchy in the network that allows faster queries after some preprocessing that basically inserts additional "shortcut"-edges into a…
The trajectory planning problem (TPP) has become increasingly crucial in the research of next-generation transportation systems, but it presents challenges due to the non-linearity of its constraints. One specific case within TPP, namely…
Global Route-Planning Algorithms (GRPA) are required to compute paths between several points located on Earth's surface. A geodesic algorithm is employed as an auxiliary tool, increasing the precision of distance calculations. This work…
In this paper, we study the problem of \textsc{Utility Driven Job Selection} on Road Networks for which the inputs are: a road network with the vertices as the set of Point-Of-Interests (Henceforth mentioned as POI) and the edges are road…
Corporations today face increasing demands for the timely and effective delivery of customer service. This creates the need for a robust and accurate automated solution to what is formally known as the ticket routing problem. This task is…
Consider the continuum of points along the edges of a network, i.e., an undirected graph with positive edge weights. We measure distance between these points in terms of the shortest path distance along the network, known as the network…
The travelling thief problem (TTP) is a well-known multi-component optimisation problem that captures the interdependence between two components: the tour across cities and the packing of items. The packing while travelling problem (PWT) is…
We present polylogarithmic approximation algorithms for variants of the Shortest Path, Group Steiner Tree, and Group ATSP problems with vector costs. In these problems, each edge e has a non-negative vector cost $c_e \in…
The Traveling Tournament Problem (TTP) is a well-known benchmark problem in the field of tournament timetabling, which asks us to design a double round-robin schedule such that each pair of teams plays one game in each other's home venue,…
Let G=(V,E) be a connected graph, where V and E represent, respectively, the node-set and the edge-set. Besides, let Q \subseteq V be a set of terminal nodes, and r \in Q be the root node of the graph. Given a weight c_{ij} \in \mathbb{N}…
Estimating the shortest travel time and providing route recommendation between different locations in a city or region can quantitatively measure the conditions of the transportation network during or after extreme events. One common…
Next Point-of-Interest (POI) recommendation plays a crucial role in urban mobility applications. Recently, POI recommendation models based on Graph Neural Networks (GNN) have been extensively studied and achieved, however, the effective…
Pedestrian trajectory prediction is critical for ensuring safety in autonomous driving, surveillance systems, and urban planning applications. While early approaches primarily focus on one-hop pairwise relationships, recent studies attempt…