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Documents authored by Kshemkalyani, Ajay D.

Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2025.63
Brief Announcement: Optimal Dispersion Under Asynchrony

Authors: Debasish Pattanayak, Ajay D. Kshemkalyani, Manish Kumar, Anisur Rahaman Molla, and Gokarna Sharma

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
We study the dispersion problem in anonymous port-labeled graphs: k ≤ n mobile agents, each with a unique ID and initially located arbitrarily on the nodes of an n-node graph with maximum degree Δ, must autonomously relocate so that no node hosts more than one agent. Dispersion serves as a fundamental task in the distributed computing of mobile agents, and its complexity stems from key challenges in local coordination under anonymity and limited memory. The goal is to minimize both the time to achieve dispersion and the memory required per agent. It is known that any algorithm requires Ω(k) time in the worst case, and Ω(log k) bits of memory per agent. A recent result [Kshemkalyani et al., 2025] gives an optimal O(k)-time algorithm in the synchronous setting and an O(k log k)-time algorithm in the asynchronous setting, both using O(log(k+Δ)) bits. We close the complexity gap in the asynchronous setting by presenting the first dispersion algorithm that runs in optimal O(k) time using O(log(k+Δ)) bits of memory per agent. Our solution relies on a novel technique for constructing a port-one tree in anonymous graphs, which may be of independent interest.
Cite as

Debasish Pattanayak, Ajay D. Kshemkalyani, Manish Kumar, Anisur Rahaman Molla, and Gokarna Sharma. Brief Announcement: Optimal Dispersion Under Asynchrony. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 63:1-63:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{pattanayak_et_al:LIPIcs.DISC.2025.63,
  author =	{Pattanayak, Debasish and Kshemkalyani, Ajay D. and Kumar, Manish and Molla, Anisur Rahaman and Sharma, Gokarna},
  title =	{{Brief Announcement: Optimal Dispersion Under Asynchrony}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{63:1--63:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.63},
  URN =		{urn:nbn:de:0030-drops-248795},
  doi =		{10.4230/LIPIcs.DISC.2025.63},
  annote =	{Keywords: Distributed algorithms, mobile agents, local communication, dispersion, asynchrony, port-one tree, time and memory complexity}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2024.50
Brief Announcement: Agent-Based Leader Election, MST, and Beyond

Authors: Ajay D. Kshemkalyani, Manish Kumar, Anisur Rahaman Molla, and Gokarna Sharma

Published in: LIPIcs, Volume 319, 38th International Symposium on Distributed Computing (DISC 2024)

Abstract
Leader election is one of the fundamental and well-studied problems in distributed computing. In this paper, we initiate the study of leader election using mobile agents. Suppose n agents are positioned initially arbitrarily on the nodes of an arbitrary, anonymous, n-node, m-edge graph G. The agents relocate themselves autonomously on the nodes of G and elect an agent as a leader such that the leader agent knows it is a leader and the other agents know they are not leaders. The objective is to minimize time and memory requirements. Following the literature, we consider the synchronous setting in which each agent performs its operations synchronously with others and hence the time complexity can be measured in rounds. The quest in this paper is to provide solutions without agents knowing any graph parameter, such as n, a priori. We first establish that, without agents knowing any graph parameter a priori, there exists a deterministic algorithm to elect an agent as a leader in O(m) rounds with O(nlog n) bits at each agent. Using this leader election result, we develop a deterministic algorithm for agents to construct a minimum spanning tree of G in O(m+nlog n) rounds using O(n log n) bits memory at each agent, without agents knowing any graph parameter a priori. Finally, using the same leader election result, we provide improved time/memory results for other fundamental distributed graph problems, namely, gathering, maximal independent set, and minimal dominating sets, removing the assumptions on agents knowing graph parameters a priori.
Cite as

Ajay D. Kshemkalyani, Manish Kumar, Anisur Rahaman Molla, and Gokarna Sharma. Brief Announcement: Agent-Based Leader Election, MST, and Beyond. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 50:1-50:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kshemkalyani_et_al:LIPIcs.DISC.2024.50,
  author =	{Kshemkalyani, Ajay D. and Kumar, Manish and Molla, Anisur Rahaman and Sharma, Gokarna},
  title =	{{Brief Announcement: Agent-Based Leader Election, MST, and Beyond}},
  booktitle =	{38th International Symposium on Distributed Computing (DISC 2024)},
  pages =	{50:1--50:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-352-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{319},
  editor =	{Alistarh, Dan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2024.50},
  URN =		{urn:nbn:de:0030-drops-212782},
  doi =		{10.4230/LIPIcs.DISC.2024.50},
  annote =	{Keywords: Distributed algorithms, mobile agents, local communication, leader election, MST, MIS, gathering, minimal dominating sets, time and memory complexity, graph parameters}
}
Document
DOI: 10.4230/LIPIcs.TIME.2023.11
Detecting Causality in the Presence of Byzantine Processes: The Synchronous Systems Case

Authors: Anshuman Misra and Ajay D. Kshemkalyani

Published in: LIPIcs, Volume 278, 30th International Symposium on Temporal Representation and Reasoning (TIME 2023)

Abstract
Detecting causality or the happens before relation between events in a distributed system is a fundamental building block for distributed applications. It was recently proved that this problem cannot be solved in an asynchronous distributed system in the presence of Byzantine processes, irrespective of whether the communication mechanism is via unicasts, multicasts, or broadcasts. In light of this impossibility result, we turn attention to synchronous systems and examine the possibility of solving the causality detection problem in such systems. In this paper, we prove that causality detection between events can be solved in the presence of Byzantine processes in a synchronous distributed system. The positive result holds for unicast, multicast, as well as broadcast modes of communication. We prove the result by providing an algorithm. Our solution uses the Replicated State Machine (RSM) approach and vector clocks.
Cite as

Anshuman Misra and Ajay D. Kshemkalyani. Detecting Causality in the Presence of Byzantine Processes: The Synchronous Systems Case. In 30th International Symposium on Temporal Representation and Reasoning (TIME 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 278, pp. 11:1-11:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{misra_et_al:LIPIcs.TIME.2023.11,
  author =	{Misra, Anshuman and Kshemkalyani, Ajay D.},
  title =	{{Detecting Causality in the Presence of Byzantine Processes: The Synchronous Systems Case}},
  booktitle =	{30th International Symposium on Temporal Representation and Reasoning (TIME 2023)},
  pages =	{11:1--11:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-298-3},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{278},
  editor =	{Artikis, Alexander and Bruse, Florian and Hunsberger, Luke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2023.11},
  URN =		{urn:nbn:de:0030-drops-191017},
  doi =		{10.4230/LIPIcs.TIME.2023.11},
  annote =	{Keywords: Byzantine fault-tolerance, causality, happens before, distributed system, message-passing, synchronous system}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2021.8
Near-Optimal Dispersion on Arbitrary Anonymous Graphs

Authors: Ajay D. Kshemkalyani and Gokarna Sharma

Published in: LIPIcs, Volume 217, 25th International Conference on Principles of Distributed Systems (OPODIS 2021)

Abstract
Given an undirected, anonymous, port-labeled graph of n memory-less nodes, m edges, and degree Δ, we consider the problem of dispersing k ≤ n robots (or tokens) positioned initially arbitrarily on one or more nodes of the graph to exactly k different nodes of the graph, one on each node. The objective is to simultaneously minimize time to achieve dispersion and memory requirement at each robot. If all k robots are positioned initially on a single node, depth first search (DFS) traversal solves this problem in O(min{m,kΔ}) time with Θ(log(k+Δ)) bits at each robot. However, if robots are positioned initially on multiple nodes, the best previously known algorithm solves this problem in O(min{m,kΔ}⋅ log 𝓁) time storing Θ(log(k+Δ)) bits at each robot, where 𝓁 ≤ k/2 is the number of multiplicity nodes in the initial configuration. In this paper, we present a novel multi-source DFS traversal algorithm solving this problem in O(min{m,kΔ}) time with Θ(log(k+Δ)) bits at each robot, improving the time bound of the best previously known algorithm by O(log 𝓁) and matching asymptotically the single-source DFS traversal bounds. This is the first algorithm for dispersion that is optimal in both time and memory in arbitrary anonymous graphs of constant degree, Δ = O(1). Furthermore, the result holds in both synchronous and asynchronous settings.
Cite as

Ajay D. Kshemkalyani and Gokarna Sharma. Near-Optimal Dispersion on Arbitrary Anonymous Graphs. In 25th International Conference on Principles of Distributed Systems (OPODIS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 217, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kshemkalyani_et_al:LIPIcs.OPODIS.2021.8,
  author =	{Kshemkalyani, Ajay D. and Sharma, Gokarna},
  title =	{{Near-Optimal Dispersion on Arbitrary Anonymous Graphs}},
  booktitle =	{25th International Conference on Principles of Distributed Systems (OPODIS 2021)},
  pages =	{8:1--8:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-219-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{217},
  editor =	{Bramas, Quentin and Gramoli, Vincent and Milani, Alessia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2021.8},
  URN =		{urn:nbn:de:0030-drops-157837},
  doi =		{10.4230/LIPIcs.OPODIS.2021.8},
  annote =	{Keywords: Distributed algorithms, Multi-agent systems, Mobile robots, Local communication, Dispersion, Exploration, Time and memory complexity}
}
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