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In the Disjoint Paths problem, the input consists of an $n$-vertex graph $G$ and a collection of $k$ vertex pairs, $\{(s_i,t_i)\}_{i=1}^k$, and the objective is to determine whether there exists a collection $\{P_i\}_{i=1}^k$ of $k$…
In the Asymmetric Traveling Salesperson Problem (ATSP) the goal is to find a closed walk of minimum cost in a directed graph visiting every vertex. We consider the approximability of ATSP on topologically restricted graphs. It has been…
Kallampally and Tewari showed in 2016 that there can be a trade-off between determinism and time in space-bounded computations. This they did by describing an unambiguous non-deterministic algorithm to solve Directed Graph Reachability that…
The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…
We investigate the problem of efficiently computing optimal transport (OT) distances, which is equivalent to the node-capacitated minimum cost maximum flow problem in a bipartite graph. We compare runtimes in computing OT distances on data…
In a temporal graph, each edge is available at specific points in time. Such an availability point is often represented by a ''temporal edge'' that can be traversed from its tail only at a specific departure time, for arriving in its head…
Traffic flow prediction is a big challenge for transportation authorities as it helps plan and develop better infrastructure. State-of-the-art models often struggle to consider the data in the best way possible, as well as intrinsic…
Graph-based nearest neighbor search methods have seen a surge of popularity in recent years, offering state-of-the-art performance across a wide variety of applications. Central to these methods is the task of constructing a sparse…
The concept of bounded highway dimension was developed to capture observed properties of the metrics of road networks. We show that a graph with bounded highway dimension, for any vertex, can be embedded into a a graph of bounded treewidth…
The goal of traffic management is efficiently utilizing network resources via adapting of source sending rates and routes selection. Traditionally, this problem is formulated into a utilization maximization problem. The single-path routing…
Graph comparison deals with identifying similarities and dissimilarities between graphs. A major obstacle is the unknown alignment of graphs, as well as the lack of accurate and inexpensive comparison metrics. In this work we introduce the…
Node connectivity plays a central role in temporal network analysis. We provide a comprehensive study of various concepts of walks in temporal graphs, that is, graphs with fixed vertex sets but edge sets changing over time. Taking into…
Consider the following distance query for an $n$-node graph $G$ undergoing edge insertions and deletions: given two sets of nodes $I$ and $J$, return the distances between every pair of nodes in $I\times J$. This query is rather general and…
Recently there has been much interest in graph-based learning, with applications in collaborative filtering for recommender networks, link prediction for social networks and fraud detection. These networks can consist of millions of…
In the coordinated motion planning problem, we are given a graph together with the starting and destination vertices of $k$ robots. At each time step, any subset of robots may move, each traversing an edge of the graph, provided that no two…
Temporal graphs are introduced to model systems where the relationships among the entities of the system evolve over time. In this paper, we consider the temporal graphs where the edge set changes with time and all the changes are known a…
A shortest-path algorithm finds a path containing the minimal cost between two vertices in a graph. A plethora of shortest-path algorithms is studied in the literature that span across multiple disciplines. This paper presents a survey of…
Traveling salesman problem is a NP-hard problem. Until now, researchers have not found a polynomial time algorithm for traveling salesman problem. Among the existing algorithms, dynamic programming algorithm can solve the problem in time…
We present a new $4$-approximation algorithm for the Combinatorial Motion Planning problem which runs in $\mathcal{O}(n^2\alpha(n^2,n))$ time, where $\alpha$ is the functional inverse of the Ackermann function, and a fully distributed…
In this work, we follow the current trend on temporal graph realization, where one is given a property P and the goal is to determine whether there is a temporal graph, that is, a graph where the edge set changes over time, with property P…