This work introduces JPS4, a novel pathfinding algorithm for 4-connected grid maps. JPS4 builds upon the Jump Point Search (JPS8) algorithm, originally designed for 8-connected environments. To achieve efficient pathfinding on 4-connected grids, JPS4 employs a canonical ordering and a successor function that enable online graph pruning. This reduces the search space by minimizing unnecessary node expansions. The core concept of JPS4 as well as JPS8 lies in the utilization of jump points. Strategically placed at obstacle corners, jump points prevent the search from overlooking crucial sections of the state space. They essentially reinitialize the canonical ordering, allowing exploration beyond obstacles. This mechanism ensures JPS4 finds optimal paths even in complex environments. The paper further explores the optimality of JPS4 and compares its performance against the established A* algorithm on various grid maps. Benchmarking results demonstrate that JPS4 significantly outperforms A* in scenarios with high obstacle density. However, A* remains more efficient on open maps. Overall, JPS4 presents itself as a promising alternative to A* for pathfinding on 4-connected grids, particularly applicable in video game development.

We present two new approaches for point prediction with streaming data. One is based on the Count-Min sketch (CMS) and the other is based on Gaussian process priors with a random bias. These methods are intended for the most general predictive problems where no true model can be usefully formulated for the data stream. In statistical contexts, this is often called the $\mathcal{M}$-open problem class. Under the assumption that the data consists of i.i.d samples from a fixed distribution function $F$, we show that the CMS-based estimates of the distribution function are consistent. We compare our new methods with two established predictors in terms of cumulative $L^1$ error. One is based on the Shtarkov solution (often called the normalized maximum likelihood) in the normal experts setting and the other is based on Dirichlet process priors. These comparisons are for two cases. The first is one-pass meaning that the updating of the predictors is done using the fact that the CMS is a sketch. For predictors that are not one-pass, we use streaming $K$-means to give a representative subset of fixed size that can be updated as data accumulate. Preliminary computational work suggests that the one-pass median version of the CMS method is rarely outperformed by the other methods for sufficiently complex data. We also find that predictors based on Gaussian process priors with random biases perform well. The Shtarkov predictors we use here did not perform as well probably because we were only using the simplest example. The other predictors seemed to perform well mainly when the data did not look like they came from an M-open data generator.

JPS (Jump Point Search) is a state-of-the-art optimal algorithm for online grid-based pathfinding. Widely used in games and other navigation scenarios, JPS nevertheless can exhibit pathological behaviours which are not well studied: (i) it may repeatedly scan the same area of the map to find successors; (ii) it may generate and expand suboptimal search nodes. In this work, we examine the source of these pathological behaviours, show how they can occur in practice, and propose a purely online approach, called Constrained JPS (CJPS), to tackle them efficiently. Experimental results show that CJPS has low overheads and is often faster than JPS in dynamically changing grid environments: by up to 7x in large game maps and up to 14x in pathological scenarios.

Jump Point Search (JPS) is a well known symmetry-breaking algorithm that can substantially improve performance for grid-based optimal pathfinding. When the input grid is static further speedups can be obtained by combining JPS with goal bounding techniques such as Geometric Containers (instantiated as Bounding Boxes) and Compressed Path Databases. Two such methods, JPS+BB and Two-Oracle Path PlannING (Topping), are currently among the fastest known approaches for computing shortest paths on grids. The principal drawback for these algorithms is the overhead costs: each one requires an all-pairs precomputation step, the running time and subsequent storage costs of which can be prohibitive. In this work we consider an alternative approach where we precompute and store goal bounding data only for grid cells which are also jump points. Since the number of jump points is usually much smaller than the total number of grid cells, we can save up to orders of magnitude in preprocessing time and space. Considerable precomputation savings do not necessarily mean performance degradation. For a second contribution we show how canonical orderings, partial expansion strategies and enhanced intermediate pruning can be leveraged to improve online query performance despite a reduction in preprocessed data. The combination of faster preprocessing and stronger online reasoning leads to three new and highly performant algorithms: JPS+BB+ and Two-Oracle Pathfinding Search (TOPS) based on search, and Topping+ based on path extraction. We give a theoretical analysis showing that each method is complete and optimal. We also report convincing gains in a comprehensive empirical evaluation that includes almost all current and cutting-edge algorithms for grid-based pathfinding.

RoboCup-2001 was the Fifth International RoboCup Competition and Conference. It was held for the first time in the United States, following RoboCup-2000 in Melbourne, Australia; RoboCup-99 in Stockholm; RoboCup-98 in Paris; and RoboCup-97 in Osaka. It was held for the first time in the United States, following RoboCup-2000 in Melbourne, Australia; RoboCup-99 in Stockholm; RoboCup-98 in Paris; and RoboCup-97 in Osaka. RoboCup is a research-oriented initiative that pioneered the field of multirobot research of robot teams starting in 1996. In those days, most of the robotics research was focused on single-robot issues.

In many navigational domains the traversability of cells is conditioned on the path taken. This is often the case in videogames, in which a character may need to acquire a certain object (i.e., a key or a flying suit) to be able to traverse specific locations (e.g., doors or high walls). In order for non-player characters to handle such scenarios we present InvJPS, an “inventory-driven” pathfinding approach based on the highly successful grid-based Jump-Point-Search (JPS) algorithm. We show, formally and experimentally, that the InvJPS preserves JPS’s optimality guarantees and its symmetry breaking advantages in inventory-based variants of game maps.

Markov jump processes (MJPs) are used to model a wide range of phenomena from disease progression to RNA path folding. However, maximum likelihood estimation of parametric models leads to degenerate trajectories and inferential performance is poor in nonparametric models. We take a small-variance asymptotics (SVA) approach to overcome these limitations. We derive the small-variance asymptotics for parametric and nonparametric MJPs for both directly observed and hidden state models. In the parametric case we obtain a novel objective function which leads to non-degenerate trajectories. To derive the nonparametric version we introduce the gamma-gamma process, a novel extension to the gamma-exponential process. We propose algorithms for each of these formulations, which we call \emph{JUMP-means}. Our experiments demonstrate that JUMP-means is competitive with or outperforms widely used MJP inference approaches in terms of both speed and reconstruction accuracy.

The Grid-Based Path Planning Competition has just completed its third iteration. The entriesused in the competition have improved significantly during this time, changing the view ofthe state of the art of grid-based pathfinding. Furthermore, the entries from the competition have beenmade publicly available, improving the ability of researchers to compare their work. Thispaper summarizes the entries to the 2014 competition, presents the 2014 competition results,and talks about what has been learned and where there is room for improvement.

Pathfinding in uniform-cost grid environments is a problem commonly found in application areas such as robotics and video games. The state-of-the-art is dominated by hierarchical pathfinding algorithms which are fast and have small memory overheads but usually return suboptimal paths. In this paper we present a novel search strategy, specific to grids, which is fast, optimal and requires no memory overhead. Our algorithm can be described as a macro operator which identifies and selectively expands only certain nodes in a grid map which we call jump points. Intermediate nodes on a path connecting two jump points are never expanded. We prove that this approach always computes optimal solutions and then undertake a thorough empirical analysis, comparing our method with related works from the literature. We find that searching with jump points can speed up A* by an order of magnitude and more and report significant improvement over the current state of the art.

To estimate the changing structure of a varying-coefficient varying-structure (VCVS) model remains an important and open problem in dynamic system modelling, which includes learning trajectories of stock prices, or uncovering the topology of an evolving gene network. In this paper, we investigate sparsistent learning of a sub-family of this model --- piecewise constant VCVS models. We analyze two main issues in this problem: inferring time points where structural changes occur and estimating model structure (i.e., model selection) on each of the constant segments. We propose a two-stage adaptive procedure, which first identifies jump points of structural changes and then identifies relevant covariates to a response on each of the segments. We provide an asymptotic analysis of the procedure, showing that with the increasing sample size, number of structural changes, and number of variables, the true model can be consistently selected. We demonstrate the performance of the method on synthetic data and apply it to the brain computer interface dataset. We also consider how this applies to structure estimation of time-varying probabilistic graphical models.