2026-09-21T06:27:58Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/823982022-01-13T07:54:01Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Nancy Lynch.
Radeva, Tsvetomira
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2013-11-18T19:18:13Z
2013-11-18T19:18:13Z
2013
2013
http://hdl.handle.net/1721.1/82398
862110423
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 75-77).
We present two link-reversal algorithms and some interesting properties that they satisfy. First, we describe the Partial Reversal (PR) algorithm [13], which ensures that the underlying graph structure is destination-oriented and acyclic. These properties of PR make it useful in routing protocols and algorithms for solving leader election and mutual exclusion. While proofs exist to establish the acyclicity property of PR, they rely on assigning labels to either the nodes or the edges in the graph. In this work we present simpler direct proof of the acyclicity property of partial reversal without using any external or dynamic labeling mechanisms. Second, we describe the leader election (LE) algorithm of [16], which guarantees that a unique leader is elected in an asynchronous network with a dynamically-changing communication topology. The algorithm ensures that, no matter what pattern of topology changes occurs, if topology changes cease, then eventually every connected component contains a unique leader and all nodes have directed paths to that leader. Our contribution includes a complexity analysis of the algorithm showing that after topology changes stop, no more than 0(n) elections occur in the system. We also provide a discussion on certain situations in which a new leader is elected (unnecessarily) when there is already another leader in the same connected component. Finally, we show how the LE algorithm can be augmented in such a way that nodes also have the shortest path to the leader.
by Tsvetomira Radeva
S.M.
77 p.
eng
Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Electrical Engineering and Computer Science.
Properties of link reversal algorithms for routing and leader election
Thesis
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<Abstract>We present two link-reversal algorithms and some interesting properties that they satisfy. First, we describe the Partial Reversal (PR) algorithm [13], which ensures that the underlying graph structure is destination-oriented and acyclic. These properties of PR make it useful in routing protocols and algorithms for solving leader election and mutual exclusion. While proofs exist to establish the acyclicity property of PR, they rely on assigning labels to either the nodes or the edges in the graph. In this work we present simpler direct proof of the acyclicity property of partial reversal without using any external or dynamic labeling mechanisms. Second, we describe the leader election (LE) algorithm of [16], which guarantees that a unique leader is elected in an asynchronous network with a dynamically-changing communication topology. The algorithm ensures that, no matter what pattern of topology changes occurs, if topology changes cease, then eventually every connected component contains a unique leader and all nodes have directed paths to that leader. Our contribution includes a complexity analysis of the algorithm showing that after topology changes stop, no more than 0(n) elections occur in the system. We also provide a discussion on certain situations in which a new leader is elected (unnecessarily) when there is already another leader in the same connected component. Finally, we show how the LE algorithm can be augmented in such a way that nodes also have the shortest path to the leader.</Abstract>
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