arXiv subjects

Dmitry Rabinovich

Publications and source records attributed to Dmitry Rabinovich.

4 recordsLinked to original sources

arXiv2024

Patrolling Grids with a Bit of Memory

This work addresses the challenge of patrolling regular grid graphs of any dimension using a single mobile agent with minimal memory and limited sensing range. We show that it is impossible to patrol some grid graphs with $0$ bits of memory, regardless of sensing range, and give an exact characterization of those grid graphs that can be patrolled with $0$ bits of memory and sensing range $V$. On the other hand, we show that an algorithm exists using $1$ bit of memory and $V=1$ that patrols any $d$-dimensional grid graph. This result is surprising given that the agent must be able to move in $2d$ distinct directions to patrol, while $1$ bit of memory allows specifying only two directions per sensory input. Our $1$-bit patrolling algorithm handles this by carefully exploiting a small state-space to access all the needed directions while avoiding getting stuck. Overall, our results give concrete evidence that extremely little memory is needed for patrolling highly regular environments like grid graphs compared to arbitrary graphs. The techniques we use, such as partitioning the environment into sensing regions and exploiting distinct coordinates resulting from higher-dimensionality, may be applicable to analyzing the space complexity of patrolling in other types of regular environments as well.

cs.RO↗

arXiv2022

Optimal Physical Sorting of Mobile Agents

Given a collection of red and blue mobile agents located on two grid rows, we seek to move all the blue agents to the far left side and all the red agents to the far right side, thus \textit{physically sorting} them according to color. The agents all start on the bottom row. They move simultaneously at discrete time steps and must not collide. Our goal is to design a centralized algorithm that controls the agents so as to sort them in the least number of time steps. We derive an \textbf{exact} lower bound on the amount of time any algorithm requires to sort a given initial configuration of agents. We find an instance optimal algorithm that provably matches this lower bound, attaining the best possible sorting time for any initial configuration. Surprisingly, we find that whenever the leftmost agent is red and the rightmost agent is blue, a straightforward decentralized and local sensing-based algorithm is at most $1$ time step slower than the centralized instance-optimal algorithm.

cs.DM↗

arXiv2022

Emerging cooperation on the road by myopic local interactions

We study a combinatorial problem inspired by the following scenario: fully autonomous vehicles drive on a multi-lane ($m \geq 2$) road. Each vehicle heads to its own destination and is allowed to exit the road only through a single designated off-ramp lane. However, an individual vehicle has a severely limited memory and sensing capabilities, and, moreover, does not communicate with its peers. In this work we present a distributed algorithm that, nonetheless, allows vehicles to get to the desired lane without collisions and in timely manner.

cs.MA↗

arXiv2019

Erratic Extremism causes Dynamic Consensus (a new model for one-dimensional opinion dynamics)

A society of agents, with ideological positions, or "opinions" measured by real values ranging from $-\infty$ (the "far left") to $+\infty$ (the "far right"), is considered. At fixed (unit) time intervals agents repeatedly reconsider and change their opinions if and only if they find themselves at the extremes of the range of ideological positions held by members of the society. Extremist agents are erratic: they become either more radical, and move away from the positions of other agents, with probability $\varepsilon$, or more moderate, and move towards the positions held by peers, with probability $(1 - \varepsilon)$. The change in the opinion of the extremists is one unit on the real line. We prove that the agent positions cluster in time, with all non-extremist agents located within a unit interval. However, the consensus opinion is dynamic. Due to the extremists' erratic behavior the clustered opinion set performs a "sluggish" random walk on the entire range of possible ideological positions (the real line). The inertia of the group, the reluctance of the society's agents to change their consensus opinion, increases with the size of the group. The extremists perform biased random walk excursions to the right and left and, in time, their actions succeed to move the society of agents in random directions. The "far left" agent effectively pushes the group consensus toward the right, while the "far right" agent counter-balances the push and causes the consensus to move toward the left. We believe that this model, and some of its variations, has the potential to explain the real world swings in societal ideologies that we see around us.

cs.MA↗