Related papers: Using Quadrilaterals to Compute the Shortest Path
Anytime heuristic search algorithms try to find a (potentially suboptimal) solution as quickly as possible and then work to find better and better solutions until an optimal solution is obtained or time is exhausted. The most widely-known…
Given a set of pairwise disjoint polygonal obstacles in the plane, finding an obstacle-avoiding Euclidean shortest path between two points is a classical problem in computational geometry and has been studied extensively. Previously,…
In the thesis, we use a recently developed tight characterisation of quantum query complexity, the adversary bound, to develop new quantum algorithms and lower bounds. Our results are as follows: * We develop a new technique for the…
The problem of navigating a bipedal robot to a desired destination in various environments is very important. However, it is very difficult to solve the navigation problem in real time because the computation time is very long due to the…
The Constraint Shortest Path (CSP) problem is as follows. An $n$-vertex graph is given, each edge/arc assigned two weights. Let us call them "cost" and "length" for definiteness. Finding a min-cost upper-bounded length path between a given…
In this paper, we introduce a graph matching method that can account for constraints of arbitrary order, with arbitrary potential functions. Unlike previous decomposition approaches that rely on the graph structures, we introduce a…
Production systems use heuristics because they are faster or scale better than their optimal counterparts. Yet, practitioners are often unaware of the performance gap between a heuristic and the optimum or between two heuristics in…
Autonomous path planning requires a synergy between global reasoning and geometric precision, especially in complex or cluttered environments. While classical A* is valued for its optimality, it incurs prohibitive computational and memory…
Routing problems such as Hamiltonian Path Problem (HPP), seeks a path to visit all the vertices in a graph while minimizing the path cost. This paper studies a variant, HPP with Probabilistic Terminals (HPP-PT), where each vertex has a…
This paper addresses the problem of finding multiple near-optimal, spatially-dissimilar paths that can be considered as alternatives in the decision making process, for finding optimal corridors in which to construct a new road. We further…
The Multi-objective Shortest Path (MOSP) problem is a classic network optimization problem that aims to find all Pareto-optimal paths between two points in a graph with multiple edge costs. Recent studies on multi-objective search with A*…
Answering the shortest-path distance between two arbitrary locations is a fundamental problem in road networks. Labelling-based solutions are the current state-of-the-arts to render fast response time, which can generally be categorised…
In imitation learning for planning, parameters of heuristic functions are optimized against a set of solved problem instances. This work revisits the necessary and sufficient conditions of strictly optimally efficient heuristics for forward…
Given a set of $n$ points on a plane, in the Minimum Weight Triangulation problem, we wish to find a triangulation that minimizes the sum of Euclidean length of its edges. This incredibly challenging problem has been studied for more than…
While the shortest path problem has myriad applications, the computational efficiency of suitable algorithms depends intimately on the underlying problem domain. In this paper, we focus on domains where evaluating the edge weight function…
A new heuristic for rectilinear crossing minimization is proposed. It is based on the idea of iteratively repositioning nodes after a first initial graph drawing. The new position of a node is computed by casting rays from the node towards…
This paper addresses the problem of finding shortest paths homotopic to a given disjoint set of paths that wind amongst point obstacles in the plane. We present a faster algorithm than previously known.
This paper introduces a novel algorithm combination designed for fast one-to-many multicriteria shortest path search. A preprocessing algorithm excludes irrelevant vertices by building a smaller cover graph. A modified version of…
In several important routing contexts it is required to identify a set of routes, each of which optimizes a different criterion. For instance, in the context of vehicle routing, one route would minimize the total distance traveled, while…
Heuristic search-based motion planning algorithms typically discretise the search space in order to solve the shortest path problem. Their performance is closely related to this discretisation. A fine discretisation allows for better…