Related papers: Heuristic Contraction Hierarchies with Approximati…
We study the problem of estimating the trace of a matrix $A$ that can only be accessed through matrix-vector multiplication. We introduce a new randomized algorithm, Hutch++, which computes a $(1 \pm \epsilon)$ approximation to $tr(A)$ for…
We introduce a new heuristic for the A* algorithm that references a data structure much smaller than the one required by the ALT heuristic. This heuristic's benefits are permitted by a new approach for computing lower bounds using…
Path-planning algorithms are an important part of a wide variety of robotic applications, such as mobile robot navigation and robot arm manipulation. However, in large search spaces in which local traps may exist, it remains challenging to…
This work establishes the technical fundamentals of a well-tuned Customizable Contraction Hierarchies (CCH) implementation that is simple and elegant. We give a detailed overview of the state of the art of CCH, review recent advances on CCH…
Hierarchical clustering is a critical task in numerous domains. Many approaches are based on heuristics and the properties of the resulting clusterings are studied post hoc. However, in several applications, there is a natural cost function…
All parallel algorithms for directed reachability and shortest paths crucially rely on efficient shortcut constructions. These constructions find directed paths and shortcut them by adding edges, with the goal to reduce the diameter of the…
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…
Fastest-path queries between two points in a very large road map is an increasingly important primitive in modern transportation and navigation systems, thus very efficient computation of these paths is critical for system performance and…
Motivated by the development of computer theory, the sorting algorithm is emerging in an endless stream. Inspired by decrease and conquer method, we propose a brand new sorting algorithmUltimately Heapsort. The algorithm consists of two…
Thresholding--the pruning of nodes or edges based on their properties or weights--is an essential preprocessing tool for extracting interpretable structure from complex network data, yet existing methods face several key limitations.…
The construction of $r$-nets offers a powerful tool in computational and metric geometry. We focus on high-dimensional spaces and present a new randomized algorithm which efficiently computes approximate $r$-nets with respect to Euclidean…
We design a heuristic method, a genetic algorithm, for the computation of an upper bound of the minimum distance of a linear code over a finite field. By the use of the row reduced echelon form, we obtain a permutation encoding of the…
We introduce a new heuristic algorithm for the problem of finding minimum size loop cutsets in multiply connected belief networks. We compare this algorithm to that proposed in [Suemmondt and Cooper, 1988]. We provide lower bounds on the…
In this paper, we study a number of well-known combinatorial optimization problems that fit in the following paradigm: the input is a collection of (potentially inconsistent) local relationships between the elements of a ground set (e.g.,…
Stochastic sequential decision making often requires hierarchical structure in the problem where each high-level action should be further planned with primitive states and actions. In addition, many real-world applications require a plan…
Network compression is crucial to making the deep networks to be more efficient, faster, and generalizable to low-end hardware. Current network compression methods have two open problems: first, there lacks a theoretical framework to…
Recent years have witnessed a tremendous growth using topological summaries, especially the persistence diagrams (encoding the so-called persistent homology) for analyzing complex shapes. Intuitively, persistent homology maps a potentially…
Column generation is an iterative method used to solve a variety of optimization problems. It decomposes the problem into two parts: a master problem, and one or more pricing problems (PP). The total computing time taken by the method is…
This paper presents a novel multicriteria shortest path search algorithm called Hierarchical MLS. The distinguishing feature of the algorithm is the multilayered structure of compressed k-Path-Cover graphs it operates on. In addition to…
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…