The drinking philosophers problem
ACM Transactions on Programming Languages and Systems (TOPLAS) - Lecture notes in computer science Vol. 174
A tree-based algorithm for distributed mutual exclusion
ACM Transactions on Computer Systems (TOCS)
Concurrency in heavily loaded neighborhood-constrained systems
ACM Transactions on Programming Languages and Systems (TOPLAS)
A log (N) distributed mutual exclusion algorithm based on path reversal
Journal of Parallel and Distributed Computing
Leader election algorithms for mobile ad hoc networks
DIALM '00 Proceedings of the 4th international workshop on Discrete algorithms and methods for mobile computing and communications
A mutual exclusion algorithm for ad hoc mobile networks
Wireless Networks
Analysis of Distributed Algorithms based on Recurrence Relations (Preliminary Version)
WDAG '91 Proceedings of the 5th International Workshop on Distributed Algorithms
Analysis of link reversal routing algorithms for mobile ad hoc networks
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
A Highly Adaptive Distributed Routing Algorithm for Mobile Wireless Networks
INFOCOM '97 Proceedings of the INFOCOM '97. Sixteenth Annual Joint Conference of the IEEE Computer and Communications Societies. Driving the Information Revolution
GeoTORA: a protocol for geocasting in mobile ad hoc networks
ICNP '00 Proceedings of the 2000 International Conference on Network Protocols
Analysis of Link Reversal Routing Algorithms
SIAM Journal on Computing
Self-Stabilizing Distributed Queuing
IEEE Transactions on Parallel and Distributed Systems
A Self-Stabilizing Leader Election Algorithm in Highly Dynamic Ad Hoc Mobile Networks
IEEE Transactions on Parallel and Distributed Systems
Proceedings of the twenty-first annual symposium on Parallelism in algorithms and architectures
An asynchronous leader election algorithm for dynamic networks
IPDPS '09 Proceedings of the 2009 IEEE International Symposium on Parallel&Distributed Processing
Link Reversal: How to Play Better to Work Less
Algorithmic Aspects of Wireless Sensor Networks
A provably starvation-free distributed directory protocol
SSS'10 Proceedings of the 12th international conference on Stabilization, safety, and security of distributed systems
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
Transience bounds for distributed algorithms
FORMATS'13 Proceedings of the 11th international conference on Formal Modeling and Analysis of Timed Systems
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Link reversal is a versatile algorithm design paradigm, originally proposed by Gafni and Bertsekas in 1981 for routing, and subsequently applied to other problems includingmutual exclusion and resource allocation. Although these algorithms arewell-known, until nowthere have been only preliminary results on time complexity, even for the simplest link reversal scheme for routing, called FullReversal (FR). In this paper we tackle this open question for arbitrary communication graphs. Our central technical insight is to describe the behavior of FR as a dynamical system, and to observe that this systemis linear in the min-plus algebra. Fromthis characterization, we derive the first exact formula for the time complexity: Given any node in any (acyclic) graph, we present an exact formula for the time complexity of that node, in terms of some simple properties of the graph. These results for FR are instrumental in analyzing a broader class of link reversal routing algorithms, as we show in a companion paper that such algorithms can be reduced to FR. In the current paper, we further demonstrate the utility of our formulas by using them to show the previously unknown fact that FR is time-efficient when executed on trees.