Related papers: Walk versus Wait: The Lazy Mathematician Wins
When providing directions to a place, web and mobile mapping services are all able to suggest the shortest route. The goal of this work is to automatically suggest routes that are not only short but also emotionally pleasant. To quantify…
The worthwhile-to-move incremental principle is a mechanism where, at each step, the agent, before moving and after exploration around the current state, compares intermediate advantages and costs to change to advantages and costs to stay.…
Humans typically walk at low speeds and run at higher speeds. Previous studies of transitions between walking and running were mostly on treadmills, but real-world locomotion allows more flexibility. Here, we study overground locomotion…
The orienteering problem is a well-studied and fundamental problem in transportation science. In the problem, we are given a graph with prizes on the nodes and lengths on the edges, together with a budget on the overall tour length. The…
We study a wireless jamming problem consisting of the competition between a legitimate receiver and a jammer, as a zero-sum game where the value to maximize/minimize is the channel capacity at the receiver's side. Most of the approaches…
Random walks on lattices with preferential relocation to previously visited sites provide a simple framework for modeling the displacements of animals and humans. When the lattice contains a few impurities or resource sites where the walker…
We consider a self-interacting process described in terms of a single-server system with service stations at each point of the real line. The customer arrivals are given by a Poisson point processes on the space-time half plane. The server…
Deterministic walk in an excited random environment is a non-Markov integer-valued process $(X_n)_{n=0}^{\infty}$, whose jump at time $n$ depends on the number of visits to the site $X_n$. The environment can be understood as stacks of…
The remaining travel time of a plane shortens with every minute that passes from its departure, and a flame diminishes a candle with every second it burns. Such everyday occurrences bias us to think that processes which have already begun…
Random walks on graphs can be slow. To speed them up, imagine that at each step instead of choosing the neighbor at random, there is a small probability $\varepsilon>0$ that we can choose it. We show that in this case, at least for graphs…
Random walks are the simplest way to explore or search a graph, and have revealed a very useful tool to investigate and characterize the structural properties of complex networks from the real world, e.g. they have been used to identify the…
The L\'evy walk, a type of random walk characterized by linear step lengths that follow a power-law distribution, is observed in the migratory behaviors of various organisms, ranging from bacteria to humans. Notably, L\'evy walks with power…
Estimation of link travel time correlation of a bus route is essential to many bus operation applications, such as timetable scheduling, travel time forecasting and transit service assessment/improvement. Most previous studies rely on…
We consider a hide-and-seek game between a Hider and a Seeker over a finite set of locations. The Hider chooses one location to conceal a stationary treasure, while the Seeker visits the locations sequentially along a route. As the search…
In two intersecting many-particle streams, one can often find the emergence of oscillatory patterns. Here, we investigate the interaction of pedestrians with vehicles, when they try to cross a road. A numerical study of this coupled…
Motivated by a problem posed by Aldous, our goal is to find the maximal-entropy win-martingale: In a sports game between two teams, the chance the home team wins is initially $x_0 \in (0,1)$ and finally 0 or 1. As an idealization we take a…
A mobile agent has to reach a target in the Euclidean plane. Both the agent and the target are modeled as points. In the beginning, the agent is at distance at most $D>0$ from the target. Reaching the target means that the agent gets at a…
We consider the online traveling salesman problem on the real line (OLTSPL) in which a salesman begins at the origin, traveling at no faster than unit speed along the real line, and wants to serve a sequence of requests, arriving online…
This paper presents an event-driven way finding algorithm for pedestrians in an evacuation scenario, which operates on a graph-based structure. The motivation of each pedestrian is to leave the facility. The events used to redirect…
We study exploration properties of a random walk on a network. For a fully connected network we find that the problem can be mapped to the well known coupon collector problem, thus allowing us to estimate form of $P(S,t)$: the distribution…