arXiv subjects

Bibhuti Das

Publications and source records attributed to Bibhuti Das.

6 recordsLinked to original sources

arXiv2026

Universal Rendezvous of Anonymous Agents with Footprints

Deterministic rendezvous for two anonymous mobile agents starting simultaneously from two distinct nodes of an anonymous connected graph and navigating synchronously in the graph requires that they meet at some node. An instance of the rendezvous problem is the underlying graph, together with two distinct nodes that are the initial positions of the agents. Such an instance is said to be feasible if there is a deterministic algorithm guaranteeing rendezvous, possibly valid only for this instance. A rendezvous algorithm is said to be universal for a class of instances if it guarantees rendezvous for all feasible instances from this class. We consider the model with footprints: whenever an agent visits an unmarked node, it leaves a permanent footprint on it, and all footprints are identical. This paper aims at answering the open problem from the paper by Das and Pelc (SPAA 2026), asking whether there exists a universal rendezvous algorithm for the class of all instances in the model with footprints. We propose a universal rendezvous algorithm for the class of all instances where the underlying graph is connected (finite or countably infinite) in the model with footprints. This shows the existence of a universal algorithm for the class of all instances in the model with footprints, which is an affirmative answer to the open problem.

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arXiv2026

Rendezvous of Mobile Deterministic Automata in Graphs

Two mobile agents, modeled as identical deterministic finite automata (DFA) navigating in synchronous rounds in a graph with unlabeled nodes, have to meet at some node. The well-researched task of meeting in a graph is known as rendezvous. Agents start at adversarially chosen distinct nodes in possibly different rounds. An instance of the rendezvous problem is the underlying graph, together with the initial nodes $u$ and $v$ of the agents. Such an instance is feasible, if there exists a DFA (possibly working only for this instance), such that its identical copies starting at nodes $u$ and $v$, with an arbitrary delay, accomplish rendezvous. A DFA is RV-universal for a class of instances, if it guarantees rendezvous of its copies starting at the designated nodes with arbitrary delay, for all feasible instances of this class. Our goal is to investigate the existence of RV-universal DFA. We start by observing that if agents cannot mark nodes in any way then there does not exist a RV-universal DFA even for the class of instances where the underlying graph is a line. Hence we allow the use of identical pebbles to mark the nodes by the agents. We consider stationary pebbles that can be dropped by agents at nodes but cannot be picked up, and movable pebbles that can be dropped by agents and later picked up. We observe that, even in the more powerful scenario of movable pebbles, if agents are equipped with any finite number of pebbles, there is no RV-universal DFA for the class of all instances. Hence we restrict attention to instances where the underlying graph is a tree. Our main contribution are two contrasting results showing that movability of pebbles is a crucial feature. We first prove that for any finite number of stationary pebbles there is no RV-universal DFA for trees, and then we design a RV-universal DFA for trees, where each agent is equipped with a single movable pebble.

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arXiv2026

Min-Sum Uniform Coverage Problem by Autonomous Mobile Robots

We study the \textit{min-sum uniform coverage} problem for a swarm of $n$ mobile robots on a given finite line segment and on a circle having finite positive radius, where the circle is given as an input. The robots must coordinate their movements to reach a uniformly spaced configuration that minimizes the total distance traveled by all robots. The robots are autonomous, anonymous, identical, and homogeneous, and operate under the \textit{Look-Compute-Move} (LCM) model with \textit{non-rigid} motion controlled by a fair asynchronous scheduler. They are oblivious and silent, possessing neither persistent memory nor a means of explicit communication. In the \textbf{line-segment setting}, the \textit{min-sum uniform coverage} problem requires placing the robots at uniformly spaced points along the segment so as to minimize the total distance traveled by all robots. In the \textbf{circle setting} for this problem, the robots have to arrange themselves uniformly around the given circle to form a regular $n$-gon. There is no fixed orientation or designated starting vertex, and the goal is to minimize the total distance traveled by all the robots. We present a deterministic distributed algorithm that achieves uniform coverage in the line-segment setting with minimum total movement cost. For the circle setting, we characterize all initial configurations for which the \textit{min-sum uniform coverage} problem is deterministically unsolvable under the considered robot model. For all the other remaining configurations, we provide a deterministic distributed algorithm that achieves uniform coverage while minimizing the total distance traveled. These results characterize the deterministic solvability of min-sum coverage for oblivious robots and achieve optimal cost whenever solvable.

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arXiv2024

Optimal Dispersion of Silent Robots in a Ring

Given a set of co-located mobile robots in an unknown anonymous graph, the robots must relocate themselves in distinct graph nodes to solve the dispersion problem. In this paper, we consider the dispersion problem for silent robots \cite{gorain2024collaborative}, i.e., no direct, explicit communication between any two robots placed in the nodes of an oriented $n$ node ring network. The robots operate in synchronous rounds. The dispersion problem for silent mobile robots has been studied in arbitrary graphs where the robots start from a single source. In this paper, we focus on the dispersion problem for silent mobile robots where robots can start from multiple sources. The robots have unique labels from a range $[0,\;L]$ for some positive integer $L$. Any two co-located robots do not have the information about the label of the other robot. The robots have weak multiplicity detection capability, which means they can determine if it is alone on a node. The robots are assumed to be able to identify an increase or decrease in the number of robots present on a node in a particular round. However, the robots can not get the exact number of increase or decrease in the number of robots. We have proposed a deterministic distributed algorithm that solves the dispersion of $k$ robots in an oriented ring in $O(\log L+k)$ synchronous rounds with $O(\log L)$ bits of memory for each robot. A lower bound $Ω(\log L+k)$ on time for the dispersion of $k$ robots on a ring network is presented to establish the optimality of the proposed algorithm.

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arXiv2022

Gathering over Meeting Nodes in Infinite Grid

The gathering over meeting nodes problem asks the robots to gather at one of the pre-defined meeting nodes. The robots are deployed on the nodes of an anonymous two-dimensional infinite grid which has a subset of nodes marked as meeting nodes. Robots are identical, autonomous, anonymous and oblivious. They operate under an asynchronous scheduler. They do not have any agreement on a global coordinate system. All the initial configurations for which the problem is deterministically unsolvable have been characterized. A deterministic distributed algorithm has been proposed to solve the problem for the remaining configurations. The efficiency of the proposed algorithm is studied in terms of the number of moves required for gathering. A lower bound concerning the total number of moves required to solve the gathering problem has been derived.

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arXiv2022

Optimal Gathering over Weber Meeting Nodes in Infinite Grid

The gathering over meeting nodes problem requires the robots to gather at one of the pre-defined meeting nodes. This paper investigates the problem with respect to the objective function that minimizes the total number of moves made by all the robots. In other words, the sum of the distances traveled by all the robots is minimized while accomplishing the gathering task. The robots are deployed on the nodes of an anonymous two-dimensional infinite grid which has a subset of nodes marked as meeting nodes. The robots do not agree on a global coordinate system and operate under an asynchronous scheduler. A deterministic distributed algorithm has been proposed to solve the problem for all those solvable configurations, and the initial configurations for which the problem is unsolvable have been characterized. The proposed gathering algorithm is optimal with respect to the total number of moves performed by all the robots in order to finalize the gathering.

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