NDLI: Anonymous Meeting in Networks

Content Provider	Springer Nature Link
Author	Dieudonné, Yoann Pelc, Andrzej
Copyright Year	2015
Abstract	A team consisting of an unknown number of mobile agents, starting from different nodes of an unknown network, possibly at different times, have to meet at the same node. Agents are anonymous (identical), execute the same deterministic algorithm and move in synchronous rounds along links of the network. An initial configuration of agents is called gatherable if there exists a deterministic algorithm (even dedicated to this particular configuration) that achieves meeting of all agents in one node. Which configurations are gatherable and how to gather all of them deterministically by the same algorithm? We give a complete solution of this gathering problem in arbitrary networks. We characterize all gatherable configurations and give two universal deterministic gathering algorithms, i.e., algorithms that gather all gatherable configurations. The first algorithm works under the assumption that a common upper bound $$N$$ on the size of the network is known to all agents. In this case our algorithm guarantees gathering with detection, i.e., the existence of a round for any gatherable configuration, such that all agents are at the same node and all declare that gathering is accomplished. If no upper bound on the size of the network is known, we show that a universal algorithm for gathering with detection does not exist. Hence, for this harder scenario, we construct a second universal gathering algorithm, which guarantees that, for any gatherable configuration, all agents eventually get to one node and stop, although they cannot tell if gathering is over. The time of the first algorithm is polynomial in the upper bound $$N$$ on the size of the network, and the time of the second algorithm is polynomial in the (unknown) size itself. Our results have an important consequence for the leader election problem for anonymous agents in arbitrary graphs. Leader election is a fundamental symmetry breaking problem in distributed computing. Its goal is to assign, in some common round, value 1 (leader) to one of the entities and value 0 (non-leader) to all others. For anonymous agents in graphs, leader election turns out to be equivalent to gathering with detection. Hence, as a by-product, we obtain a complete solution of the leader election problem for anonymous agents in arbitrary graphs.
Starting Page	908
Ending Page	946
Page Count	39
File Format	PDF
ISSN	01784617
Journal	Algorithmica
Volume Number	74
Issue Number	2
e-ISSN	14320541
Language	English
Publisher	Springer US
Publisher Date	2015-03-04
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Gathering Deterministic algorithm Anonymous mobile agent Algorithm Analysis and Problem Complexity Theory of Computation Mathematics of Computing Algorithms Computer Systems Organization and Communication Networks Data Structures, Cryptology and Information Theory
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computer Science Applications

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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