arXiv subjects

Prabhat Kumar Chand

Publications and source records attributed to Prabhat Kumar Chand.

6 recordsLinked to original sources

arXiv2025

Improved Linear-Time Construction of Minimal Dominating Set via Mobile Agents

Mobile agents have emerged as a powerful framework for solving fundamental graph problems in distributed settings in recent times. These agents, modelled as autonomous physical or software entities, possess local computation power, finite memory and have the ability to traverse a graph, offering efficient solutions to a range of classical problems. In this work, we focus on the problem of computing a \emph{minimal dominating set} (mDS) in anonymous graphs using mobile agents. Building on the recently proposed optimal dispersion algorithm on the synchronous mobile agent model, we design two new algorithms that achieve a \emph{linear-time} solution for this problem in the synchronous setting. Specifically, given a connected $n$-node graph with $n$ agents initially placed in either rooted or arbitrary configurations, we show that an mDS can be computed in $O(n)$ rounds using only $O(\log n)$ bits of memory per agent, without using any prior knowledge of any global parameters. This improves upon the best-known complexity results in the literature over the same model. In addition, as natural by-products of our methodology, our algorithms also construct a spanning tree and elect a unique leader in $O(n)$ rounds, which are also important results of independent interest in the mobile-agent framework.

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arXiv2025

Computing Tree Structures in Anonymous Graphs via Mobile Agents

Minimum Spanning Tree (MST) and Breadth-First Search (BFS) tree constructions are classical problems in distributed computing, traditionally studied in the message-passing model, where static nodes communicate via messages. This paper investigates MST and BFS tree construction in an agent-based network, where mobile agents explore a graph and compute. Each node hosts one agent, and communication occurs when agents meet at a node. We consider $n$ agents initially dispersed (one per node) in an anonymous, arbitrary $n$-node, $m$-edge graph $G$. The goal is to construct the BFS and MST trees from this configuration such that each tree edge is known to at least one of its endpoints, while minimizing time and memory per agent. We work in a synchronous model and assume agents have no prior knowledge of any graph parameters such as $n$, $m$, $D$, $\Delta$ (graph diameter and maximum degree). Prior work solves BFS in $O(D\Delta)$ rounds with $O(\log n)$ bits per agent, assuming the root is known. We give a deterministic algorithm that constructs the BFS tree in $O(\min(D\Delta, m\log n) + n\log n + \Delta \log^2 n)$ rounds using $O(\log n)$ bits per agent without root knowledge. To determine the root, we solve leader election and MST construction. We elect a leader and construct the MST in $O(n\log n + \Delta \log^2 n)$ rounds, with $O(\log n)$ bits per agent. Prior MST algorithms require $O(m + n\log n)$ rounds and $\max(\Delta, \log n) \log n$ bits. Our results significantly improve memory efficiency and time, achieving nearly linear-time leader election and MST. Agents are assumed to know $\lambda$, the maximum identifier, bounded by a polynomial in $n$.

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arXiv2025

Distributed Butterfly Analysis using Mobile Agents

Butterflies, or 4-cycles in bipartite graphs, are crucial for identifying cohesive structures and dense subgraphs. While agent-based data mining is gaining prominence, its application to bipartite networks remains relatively unexplored. We propose distributed, agent-based algorithms for \emph{Butterfly Counting} in a bipartite graph $G((A,B),E)$. Agents first determine their respective partitions and collaboratively construct a spanning tree, electing a leader within $O(n \log \lambda)$ rounds using only $O(\log \lambda)$ bits per agent. A novel meeting mechanism between adjacent agents improves efficiency and eliminates the need for prior knowledge of the graph, requiring only the highest agent ID $\lambda$ among the $n$ agents. Notably, our techniques naturally extend to general graphs, where leader election and spanning tree construction maintain the same round and memory complexities. Building on these foundations, agents count butterflies per node in $O(\Delta)$ rounds and compute the total butterfly count of $G$ in $O(\Delta+\min\{|A|,|B|\})$ rounds.

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arXiv2024

Agent-Based Triangle Counting: Unlocking Truss Decomposition, Triangle Centrality, and Local Clustering Coefficient

Triangle counting in a graph is a fundamental problem with wide-ranging applications. It is crucial for understanding graph structure and serves as a basis for more advanced graph analytics. One key application is truss decomposition, a technique for identifying maximal, highly interconnected subgraphs, revealing structural cohesion and tight-knit communities in complex graphs. This facilitates analysis of relationships and information flow in fields such as social networks, biology, and recommendation systems. Using mobile agents or robots for tasks like truss decomposition and clustering coefficient computation is especially advantageous in decentralised environments with limited or unreliable communication. In such scenarios, agents can perform local computations without requiring an extensive communication infrastructure. This is valuable in contexts like disaster response, urban management, and military operations, where broadcast communication is impractical. In this paper, we address the triangle counting problem in an arbitrary anonymous graph using mobile agents. This method is extended as a subroutine to solve the truss decomposition problem and compute triangle centrality and the local clustering coefficient for each node. Our approach uses $n$ autonomous mobile agents, each starting at a different node of an $n$-node graph. These agents coordinate to collaboratively solve triangle enumeration, then truss decomposition, triangle centrality, and clustering coefficient. We assume a synchronous system where agents execute tasks concurrently, allowing time to be measured in rounds. The graph is anonymous (nodes have no IDs), but agents have distinct IDs and limited memory. Agents can perform local computations and communicate only when co-located. Our goal is to design algorithms that minimise both time and memory per agent, while enabling solutions to the above problems.

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arXiv2023

Run for Cover: Dominating Set via Mobile Agents

Research involving computing with mobile agents is a fast-growing field, given the advancement of technology in automated systems, e.g., robots, drones, self-driving cars, etc. Therefore, it is pressing to focus on solving classical network problems using mobile agents. In this paper, we study one such problem -- finding small dominating sets of a graph $G$ using mobile agents. Dominating set is interesting in the field of mobile agents as it opens up a way for solving various robotic problems, e.g., guarding, covering, facility location, transport routing, etc. In this paper, we first present two algorithms for computing a {\em minimal dominating set}: (i) an $O(m)$ time algorithm if the robots start from a single node (i.e., gathered initially), (ii) an $O(\ellΔ\log(λ)+n\ell+m)$ time algorithm, if the robots start from multiple nodes (i.e., positioned arbitrarily), where $m$ is the number of edges and $Δ$ is the maximum degree of $G$, $\ell$ is the number of clusters of the robot initially and $λ$ is the maximum ID-length of the robots. Then we present a $\ln (Δ)$ approximation algorithm for the {\em minimum} dominating set which takes $O(nΔ\log (λ))$ rounds.

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arXiv2022

Fault-Tolerant Dispersion of Mobile Robots

We consider the mobile robot dispersion problem in the presence of faulty robots (crash-fault). Mobile robot dispersion consists of $k\leq n$ robots in an $n$-node anonymous graph. The goal is to ensure that regardless of the initial placement of the robots over the nodes, the final configuration consists of having at most one robot at each node. In a crash-fault setting, up to $f \leq k$ robots may fail by crashing arbitrarily and subsequently lose all the information stored at the robots, rendering them unable to communicate. In this paper, we solve the dispersion problem in a crash-fault setting by considering two different initial configurations: i) the rooted configuration, and ii) the arbitrary configuration. In the rooted case, all robots are placed together at a single node at the start. The arbitrary configuration is a general configuration (a.k.a. arbitrary configuration in the literature) where the robots are placed in some $l<k$ clusters arbitrarily across the graph. For the first case, we develop an algorithm solving dispersion in the presence of faulty robots in $O(k^2)$ rounds, which improves over the previous $O(f\cdot\text{min}(m,kΔ))$-round result by \cite{PS021}. For the arbitrary configuration, we present an algorithm solving dispersion in $O((f+l)\cdot\text{min}(m, k Δ, k^2))$ rounds, when the number of edges $m$ and the maximum degree $Δ$ of the graph is known to the robots.

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