Related papers: Bilateral parking procedures
We introduce a new approach to the enumeration of rational slope parking functions with respect to the area and a generalized dinv statistics, and relate the combinatorics of parking functions to that of affine permutations. We relate our…
We develop combinatorial methods for computing the rotation distance between binary trees, i.e., equivalently, the flip distance between triangulations of a polygon. As an application, we prove that, for each n, there exist size n trees at…
Street parking spots for automobiles are a scarce commodity in most urban environments. The heterogeneity of car sizes makes it inefficient to rigidly define fixed-sized spots. Instead, unmarked streets in cities like New York leave…
Designing reliable decision strategies for autonomous urban driving is challenging. Reinforcement learning (RL) has been used to automatically derive suitable behavior in uncertain environments, but it does not provide any guarantee on the…
We apply recent ideas about complexity and randomness to the philosophy of laws and chances. We develop two ways to use algorithmic randomness to characterize probabilistic laws of nature. The first, a generative chance* law, employs a…
This paper presents an optimization procedure to choose a parking facility according to different criteria: total travel time including transfers, parking fee and a factor depending on the risk of not having an available spot in the parking…
Berget and Rhoades asked whether the permutation representation obtained by the action of $S_{n-1}$ on parking functions of length $n-1$ can be extended to a permutation action of $S_{n}$. We answer this question in the affirmative. We…
A duality between general partially ordered sets and certain topolgical spaces with two closures is established.
We consider machine learning in a comparison-based setting where we are given a set of points in a metric space, but we have no access to the actual distances between the points. Instead, we can only ask an oracle whether the distance…
We show that the number of parking functions of length $n$ with zero secondary dinv is equal to the number of ordered cycle decompositions of permutations of $[n]$.
A classical parking function of length $n$ is a list of positive integers $(a_1, a_2, \ldots, a_n)$ whose nondecreasing rearrangement $b_1 \leq b_2 \leq \cdots \leq b_n$ satisfies $b_i \leq i$. The convex hull of all parking functions of…
In this paper, the parking problem of a swarm of mobile robots has been studied. The robots are deployed at the nodes of an infinite grid, which has a subset of prefixed nodes marked as parking nodes. Each parking node p_i has a capacity of…
It is known that for the 2n-step symmetric simple random walk on Z, two events have the same probability if and only if their sets of paths have the same cardinality. In this article, we construct two kinds of bijections between sets of…
Gibbs random fields play an important role in statistics, for example the autologistic model is commonly used to model the spatial distribution of binary variables defined on a lattice. However they are complicated to work with due to an…
Intelligent systems sometimes need to infer the probable goals of people, cars, and robots, based on partial observations of their motion. This paper introduces a class of probabilistic programs for formulating and solving these problems.…
Parking accurately and safely in highly constrained spaces remains a critical challenge. Unlike structured driving environments, parking requires executing complex maneuvers such as frequent gear shifts and steering saturation. Recent…
In this paper we formulate a dynamic mixed integer program for optimally zoning curbside parking spaces subject to transportation policy-inspired constraints and regularization terms. First, we illustrate how given some objective of curb…
Parking guidance systems have recently become a popular trend as a part of the smart cities' paradigm of development. The crucial part of such systems is the algorithm allowing drivers to search for available parking lots across regions of…
We give a rigorous solution of an optimisation problem of minimizing the expected delay caused by encountering a red traffic light on a road journey. The problem incorporates simple constraints on maximum speed, acceleration and braking…
In this paper, let $\mathcal{P}_{n;\leq s;k}^l$ denote a set of $k$-flaw preference sets $(a_1,...,a_n)$ with $n$ parking spaces satisfying that $1\leq a_i\leq s$ for any $i$ and $a_1=l$ and $p_{n;\leq s;k}^l=|\mathcal{P}_{n;\leq s;k}^l|$.…