Two algorithms for maintaining order in a list
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
The Computer Journal
Detecting global termination conditions in the face of uncertainty
PODC '87 Proceedings of the sixth annual ACM Symposium on Principles of distributed computing
Fault tolerant distributed majority commitment
Journal of Algorithms
Implicit representation of graphs
SIAM Journal on Discrete Mathematics
Local management of a global resource in a communication network
Journal of the ACM (JACM)
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
A comparison of labeling schemes for ancestor queries
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Two Simplified Algorithms for Maintaining Order in a List
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Journal of Algorithms
Compact Labeling Scheme for Ancestor Queries
SIAM Journal on Computing
Object location using path separators
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Controller and estimator for dynamic networks
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Labeling schemes for weighted dynamic trees
Information and Computation
Dynamic routing schemes for graphs with low local density
ACM Transactions on Algorithms (TALG)
Upper and lower bounds for routing schemes in dynamic networks
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Compact separator decompositions in dynamic trees and applications to labeling schemes
DISC'07 Proceedings of the 21st international conference on Distributed Computing
Compact Routing Schemes for Dynamic Trees in the Fixed Port Model
ICDCN '09 Proceedings of the 10th International Conference on Distributed Computing and Networking
Labeling schemes for vertex connectivity
ACM Transactions on Algorithms (TALG)
Distributed computation in dynamic networks
Proceedings of the forty-second ACM symposium on Theory of computing
New bounds for the controller problem
DISC'09 Proceedings of the 23rd international conference on Distributed computing
Compact routing in power-law graphs
DISC'09 Proceedings of the 23rd international conference on Distributed computing
Compact ancestry labeling schemes for XML trees
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A compact routing scheme and approximate distance oracle for power-law graphs
ACM Transactions on Algorithms (TALG)
Controller and estimator for dynamic networks
Information and Computation
Sublinear-Time maintenance of breadth-first spanning tree in partially dynamic networks
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
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A classical routing problem consists of assigning a label and distinct port numbers to each node of a graph, such that for every node v, given its own label and the label of any destination vertex u, node v can find which of its incident port numbers leads to the next vertex on a shortest path connecting v and u. In the static (fixed topology) setting, such a routing scheme is evaluated by the label size, i.e., the maximal number of bits stored in a label. Naturally, special attention is given to compact schemes, which are schemes enjoying asymptotically optimal labels. Many routing schemes were proposed for the static setting. However, the more realistic and complex dynamic setting, in which topology changes may occur at arbitrary nodes, has received much less attention. In the dynamic setting, the occurrence of topology changes may force the scheme to occasionally update the (hopefully short) labels, by delivering information from place to place. This raises a natural tradeoff between the size of the labels and the number of messages required for maintaining them. The above dynamic routing problem was proposed by Afek, Gafni, and Ricklin (1989), who also presented an elegant and rather efficient dynamic routing scheme for trees, supporting one type of topology change, namely, the addition of a leaf. Various attempts for improving the tradeoff between the label size and the message complexity as well as for supporting more types of topology changes on trees, were subsequently proposed. Still, the best known compact routing scheme for dynamic trees has very high message complexity, namely, O(nε) amortized messages per topological change. Moreover, previous routing schemes for dynamic trees support at most two kinds of topology changes, namely, the addition and the removal of a leaf node. In this paper, we present two compact routing schemes for dynamic trees that incur extremely low message complexity and can support more types of topology changes than previous schemes. We first present a dynamic compact routing scheme that supports the additions of both leaves and internal nodes and incurs only O(log n) amortized message complexity per node. We then extend that scheme obtaining a dynamic compact routing scheme that supports additions of both leaves and internal nodes as well as deletions of nodes of degree at most 2. The extended scheme incurs O(log2 n) amortized message complexity per topological change.