Related papers: About Testing the Speed of Calculating the Shortes…
We present a new approach called GR (Graph Reduction) algorithm for searching loop-less k-shortest paths (1st to k-th shortest paths) in a graph based on graph reduction. Let a source vertex and a target vertex of k-shortest paths be v_s…
This work studies path planning in two-dimensional space, in the presence of polygonal obstacles. We specifically address the problem of building a roadmap graph, that is, an abstract representation of all the paths that can potentially be…
Graphs with high symmetry or regularity are the main source for experimentally hard instances of the notoriously difficult graph isomorphism problem. In this paper, we study the computational complexity of isomorphism testing for line…
We present linear time {\it in-place} algorithms for several basic and fundamental graph problems including the well-known graph search methods (like depth-first search, breadth-first search, maximum cardinality search), connectivity…
Constant-factor, polynomial-time approximation algorithms are presented for two variations of the traveling salesman problem with time windows. In the first variation, the traveling repairman problem, the goal is to find a tour that visits…
We consider efficient route planning for robots in applications such as infrastructure inspection and automated surgical imaging. These tasks can be modeled via the combinatorial problem Graph Inspection. The best known algorithms for this…
We study the optimal scheduling of graph states in measurement-based quantum computation, establishing an equivalence between measurement schedules and path decompositions of graphs. We define the spatial cost of a measurement schedule…
Despite being recognized as neurobiologically plausible, active inference faces difficulties when employed to simulate intelligent behaviour in complex environments due to its computational cost and the difficulty of specifying an…
Reconfiguring two shortest paths in a graph means modifying one shortest path to the other by changing one vertex at a time so that all the intermediate paths are also shortest paths. This problem has several natural applications, namely:…
The complexity of a CSMA algorithm has been translated to the norm properties of a dependencies matrix. The maximum throughput optimization is reformulated by including the dependencies matrix in the formulations. It has been shown that for…
Listing all triangles is a fundamental graph operation. Triangles can have important interpretations in real-world graphs, especially social and other interaction networks. Despite the lack of provably efficient (linear, or slightly…
This paper addresses the problem of planning time-optimal trajectories for multiple cooperative agents along specified paths through a static road network. Vehicle interactions at intersections create non-trivial decisions, with complex…
Algorithms which compute properties over graphs have always been of interest in computer science, with some of the fundamental algorithms, such as Dijkstra's algorithm, dating back to the 50s. Since the 70s there as been interest in…
This study investigates computationally efficient inner-loop algorithms for estimating static/dynamic BLP models. It provides the following ideas for reducing the number of inner-loop iterations: (1). Add a term relating to the outside…
The computation of time-optimal velocity profiles along prescribed paths, subject to generic acceleration constraints, is a crucial problem in robot trajectory planning, with particular relevance to autonomous racing. However, the existing…
With the recent influx in demand for multi-robot systems throughout industry and academia, there is an increasing need for faster, robust, and generalizable path planning algorithms. Similarly, given the inherent connection between control…
For vertices $u$ and $v$ of an $n$-vertex graph $G$, a $uv$-trail of $G$ is an induced $uv$-path of $G$ that is not a shortest $uv$-path of $G$. Berger, Seymour, and Spirkl [Discrete Mathematics 2021] gave the previously only known…
We consider the problem of finding lower bounds on the I/O complexity of arbitrary computations in a two level memory hierarchy. Executions of complex computations can be formalized as an evaluation order over the underlying computation…
In this paper, we present two main results. First, by only one conjecture (Conjecture 2.9) for recognizing a vertex symmetric graph, which is the hardest task for our problem, we construct an algorithm for finding an isomorphism between two…
Standard algorithms for finding the shortest path in a graph require that the cost of a path be additive in edge costs, and typically assume that costs are deterministic. We consider the problem of uncertain edge costs, with potential…