Related papers: ERA*: Enhanced Relaxed A* algorithm for Solving th…
The All-Pairs Shortest Paths (APSP) is a foundational problem in theoretical computer science. Approximating APSP in undirected unweighted graphs has been studied for many years, beginning with the work of Dor, Halperin and Zwick…
Emerging reconfigurable optical communication technologies allow to enhance datacenter topologies with demand-aware links optimized towards traffic patterns. This paper studies the algorithmic problem of jointly optimizing topology and…
The problem of finding multiple simple shortest paths in a weighted directed graph $G=(V,E)$ has many applications, and is considerably more difficult than the corresponding problem when cycles are allowed in the paths. Even for a single…
The neighbourhood matrix, $\mathcal{NM}(G)$, a novel representation of graphs proposed in \cite {ALPaper} is defined using the neighbourhood sets of the vertices. The matrix also exhibits a bijection between the product of two well-known…
A* is a classic and popular method for graphs search and path finding. It assumes the existence of a heuristic function $h(u,t)$ that estimates the shortest distance from any input node $u$ to the destination $t$. Traditionally, heuristics…
We propose a new hybrid topology optimization algorithm based on multigrid approach that combines the parallelization strategy of CPU using OpenMP and heavily multithreading capabilities of modern Graphics Processing Units (GPU). In…
The Restricted Shortest Path (RSP) problem, also known as the Delay-Constrained Least-Cost (DCLC) problem, is an NP-hard bicriteria optimization problem on graphs with $n$ vertices and $m$ edges. In a graph where each edge is assigned a…
Identifying shortest paths between nodes in a network is a common graph analysis problem that is important for many applications involving routing of resources. An adversary that can manipulate the graph structure could alter traffic…
Vehicle routing algorithms usually reformulate the road network into a complete graph in which each arc represents the shortest path between two locations. Studies on time-dependent routing followed this model and therefore defined the…
It is a critical issue to compute the shortest paths between nodes in networks. Exact algorithms for shortest paths are usually inapplicable for large scale networks due to the high computational complexity. In this paper, we propose a…
Recently, the trend of incorporating differentiable algorithms into deep learning architectures arose in machine learning research, as the fusion of neural layers and algorithmic layers has been beneficial for handling combinatorial data,…
We study the Regularized A-optimal Design (RAOD) problem, which selects a subset of $k$ experiments to minimize the inverse of the Fisher information matrix, regularized with a scaled identity matrix. RAOD has broad applications in Bayesian…
From logistics to the natural sciences, combinatorial optimisation on graphs underpins numerous real-world applications. Reinforcement learning (RL) has shown particular promise in this setting as it can adapt to specific problem structures…
Multiquery planning algorithms find paths between various different starts and goals in a single search space. They are designed to do so efficiently by reusing information across planning queries. This information may be computed before or…
This paper introduces a novel, lightweight method to solve the visibility problem for 2D grids. The proposed method evaluates the existence of lines-of-sight from a source point to all other grid cells in a single pass with no preprocessing…
We study a scenario for route planning in road networks, where the objective to be optimized may change between every shortest path query. Since this invalidates many of the known speedup techniques for road networks that are based on…
In this paper, we focus on the relaxed proximal point algorithm (RPPA) for solving convex (possibly nonsmooth) optimization problems. We conduct a comprehensive study on three types of relaxation schedules: (i) constant schedule with…
Simulated annealing (SA) is a well-known algorithm for solving combinatorial optimization problems. However, the computation time of SA increases rapidly, as the size of the problem grows. Recently, a stochastic simulated annealing (SSA)…
Integrating artificial intelligence (AI) into sampling-based motion planning provides new possibilities for improving autonomous navigation efficiency. In this paper, three algorithms, namely RRT*, Neural RRT*, and Neural Informed RRT*, are…
We consider the bi-criteria shortest-path problem where we want to compute shortest paths on a graph that simultaneously balance two cost functions. While this problem has numerous applications, there is usually no path minimizing both cost…