Related papers: New combinatorial perspectives on MVP parking func…
Naples parking functions were introduced as a generalization of classical parking functions, in which cars are allowed to park backwards, by checking up to a fixed number of previous spots, before proceeding forward as usual. In this work…
Suppose that $n$ drivers each choose a preferred parking space in a linear car park with $m$ spaces. Each driver goes to the chosen space and parks there if it is free, and otherwise takes the first available space with larger number (if…
Consider $n$ cars $C_1, C_2, \ldots, C_n$ that want to park in a parking lot with parking spaces $1,2,\ldots,n$ that appear in order. Each car $C_i$ has a parking preference $\alpha_i \in \{1,2,\ldots,n\}$. The cars appear in order, if…
In a parking function, a lucky car is a car that parks in its preferred parking spot and the parking outcome is the permutation encoding the order in which the cars park on the street. We give a characterization for the set of parking…
Existing parking recommendation solutions mainly focus on finding and suggesting parking spaces based on the unoccupied options only. However, there are other factors associated with parking spaces that can influence someone's choice of…
In a parking function, a car is considered lucky if it is able to park in its preferred spot. Extending work of Harris and Martinez, we enumerate outcomes of parking functions with a fixed set of lucky cars. We then consider a…
Smart Internet of Vehicles (IoVs) combined with Artificial Intelligence (AI) will contribute to vehicle decision-making in the Intelligent Transportation System (ITS). Multi-Vehicle Pursuit games (MVP), a multi-vehicle cooperative ability…
We introduce a generalization of parking functions called $t$-metered $(m,n)$-parking functions, in which one of $m$ cars parks among $n$ spots per hour then leaves after $t$ hours. We characterize and enumerate these sequences for $t=1$,…
Models of parking in which cars are placed randomly and then move according to a deterministic rule have been studied since the work of Konheim and Weiss in the 1960s. Recently, Damron, Gravner, Junge, Lyu, and Sivakoff introduced a model…
Interval parking functions are a generalization of parking functions in which cars have an interval preference for their parking. We generalize this definition to parking functions with $n$ cars and $m\geq n$ parking spots, which we call…
Motivated by the rapid development of autonomous vehicle technology, this work focuses on the challenges of introducing them in ride-hailing platforms with conventional strategic human drivers. We consider a ride-hailing platform that…
Two multivehicle routing problems are considered in the framework that a visit to a location must take place during a specific time window in order to be counted and all time windows are the same length. In the first problem, the goal is to…
The aim of the bi-objective multimodal car-sharing problem (BiO-MMCP) is to determine the optimal mode of transport assignment for trips and to schedule the routes of available cars and users whilst minimizing cost and maximizing user…
We study the enumeration problem for different kind of tree parking functions introduced recently, called tree parking functions, tree parking distributions, prime tree parking functions, and prime tree parking distributions, for rooted…
We recall that the $k$-Naples parking functions of length $n$ (a generalization of parking functions) are defined by requiring that a car which finds its preferred spot occupied must first back up a spot at a time (up to $k$ spots) before…
Given a strictly increasing sequence $\mathbf{t}$ with entries from $[n]:=\{1,\ldots,n\}$, a parking completion is a sequence $\mathbf{c}$ with $|\mathbf{t}|+|\mathbf{c}|=n$ and $|\{t\in \mathbf{t}\mid t\le i\}|+|\{c\in \mathbf{c}\mid c\le…
In many applications of social navigation, existing works have shown that predicting and reasoning about human intentions can help robotic agents make safer and more socially acceptable decisions. In this work, we study this problem for…
We introduce a prioritized system-optimal algorithm for mandatory lane change (MLC) behavior of connected and automated vehicles (CAV) from a dedicated lane. Our approach applies a cooperative lane change that prioritizes the decisions of…
Naples parking functions were introduced as a generalization of classical parking functions, in which cars are allowed to park backwards, by checking up to a fixed number of previous slots, before proceedings forward as usual. In our…
In this paper, we view parking functions viewed as labeled Dyck paths in order to study a notion of pattern avoidance first introduced by Remmel and Qiu. In particular we enumerate the parking functions avoiding any set of two or more…