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Labeling Schemes for Weighted Dynamic Trees [chapter]

Amos Korman, David Peleg
2003 Lecture Notes in Computer Science  
The paper considers dynamic weighted trees where the vertices of the trees are fixed but the (positive integral) weights of the edges may change.  ...  As most applications for network representations in general, and distance labeling schemes in particular, concern large and dynamically changing networks, it is of interest to focus on distributed dynamic  ...  A second result of [25] introduces a more general labeling scheme for dynamic trees, based on extending an existing static tree labeling scheme to a dynamic setting.  ... 
doi:10.1007/3-540-45061-0_31 fatcat:5a2seu3mfzcpxbzlwyqnkf73la

Labeling schemes for weighted dynamic trees

Amos Korman, David Peleg
2007 Information and Computation  
The paper considers dynamic weighted trees where the vertices of the trees are fixed but the (positive integral) weights of the edges may change.  ...  As most applications for network representations in general, and distance labeling schemes in particular, concern large and dynamically changing networks, it is of interest to focus on distributed dynamic  ...  A second result of [25] introduces a more general labeling scheme for dynamic trees, based on extending an existing static tree labeling scheme to a dynamic setting.  ... 
doi:10.1016/j.ic.2007.08.004 fatcat:ih2j3jqf2zh7rmjwpkaxxr4yny

Improved compact routing schemes for dynamic trees

Amos Korman
2008 Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing - PODC '08  
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.  ...  Still, the best known compact routing scheme for dynamic trees has very high message complexity, namely, O(n ) amortized messages per topological change.  ...  Our dynamic ancestry scheme is then used in Section 4 to construct our dynamic routing scheme for a growing tree, which assigns and maintains asymptotically optimal Θ(log n)-bit labels, and incurs O(log  ... 
doi:10.1145/1400751.1400777 dblp:conf/podc/Korman08 fatcat:37bbb4puqnh4tp34nc45gkgymy

Compact separator decompositions in dynamic trees and applications to labeling schemes

Amos Korman, David Peleg
2008 Distributed computing  
In this paper we construct an efficient scheme maintaining a separator decomposition representation in dynamic trees. Our dynamic scheme uses asymptotically optimal labels.  ...  Going along these lines, we then show how to use our dynamic separator decomposition to construct rather efficient routing schemes on dynamic trees, for both the designer and the adversary port models.  ...  Our basic dynamic separator scheme is then used in order to construct several other dynamic labeling schemes for the dynamic tree T , which improve known results.  ... 
doi:10.1007/s00446-008-0061-5 fatcat:zj3oc3y5hbbxjhp2orhb35jxa4

Compact Multicast Routing [chapter]

Ittai Abraham, Dahlia Malkhi, David Ratajczak
2009 Lecture Notes in Computer Science  
So a complete information scheme should maintain at each node the next step(s) of the shortest spanning tree, for all possible subsets.  ...  to all nodes of , divided by the weight of the minimum Steiner tree with ∪ { } as targets.  ...  Conclusions We have initiated the study of distributed compact multicast routing schemes. No lower bounds are known (other than the known ones for unicast routing).  ... 
doi:10.1007/978-3-642-04355-0_40 fatcat:kjm25bnqi5f5xpxrj72dteoiiu

Labeling Schemes with Queries [article]

Amos Korman, Shay Kutten
2006 arXiv   pre-print
An f-labeling scheme for a family of graphs labels the vertices of all graphs in such that for every graph G∈ and every two vertices u,v∈ G, the value f(u,v) can be inferred by merely inspecting the labels  ...  We show that inspecting the label of a single additional vertex (one query) enables us to reduce the label size of many labeling schemes significantly.  ...  Their schemes apply for dynamic models in which the tree topology is fixed but the edge weights may change.  ... 
arXiv:cs/0609163v1 fatcat:adtz2ulsufcrzddgmzrxjlim4q

Labeling Schemes for Dynamic Tree Networks [chapter]

Amos Korman, David Peleg, Yoav Rodeh
2002 Lecture Notes in Computer Science  
A more general labeling scheme is then introduced for the dynamic tree model, based on extending an existing static tree labeling scheme to the dynamic setting.  ...  As applications for distance labeling schemes concern mainly large and dynamically changing networks, it is of interest to study distributed dynamic labeling schemes.  ...  We then introduce a rather general labeling scheme for the dynamic tree model, based on extending an existing static tree labeling scheme to the dynamic setting.  ... 
doi:10.1007/3-540-45841-7_5 fatcat:6cckx7isjvfdnmxju62avfh7xm

Compact Routing Schemes for Dynamic Trees in the Fixed Port Model [chapter]

Amos Korman
2008 Lecture Notes in Computer Science  
We present two routing schemes for dynamic trees that maintain labels of asymptotically optimal size using extremely low average message complexity (per node).  ...  We would like to point out that the best known routing scheme for dynamic trees that maintains asymptotically optimal labels in the fixed port model has very high average message complexity, namely, O(  ...  a routing scheme with label size Θ(log n), for the family of n-node (static) trees.  ... 
doi:10.1007/978-3-540-92295-7_28 fatcat:tr6eycp2zze6howyxobug4oatu

A note on models for graph representations

Amos Korman, Shay Kutten
2009 Theoretical Computer Science  
Specifically, we consider models for labeling schemes, and discuss issues regarding the number of labels consulted vs. the sizes of the labels.  ...  Some very involved lower bounds for the sizes of the labels were proven. Also, some highly sophisticated labeling schemes were developed to ensure short labels.  ...  Their schemes apply for dynamic models in which the tree topology is fixed but the edge weights may change.  ... 
doi:10.1016/j.tcs.2008.10.036 fatcat:kbz6erdkfzfmplmsitsmzmmmoe

General Compact Labeling Schemes for Dynamic Trees [chapter]

Amos Korman
2005 Lecture Notes in Computer Science  
This paper investigates labeling schemes for dynamic trees.  ...  A general method for constructing labeling schemes for dynamic trees (under the above mentioned dynamic tree models) was previously developed in [29] .  ...  The label size of both schemes is O(log 2 n + log n log W ) where W denotes the largest edge weight in the tree.  ... 
doi:10.1007/11561927_33 fatcat:loybwspw6ngobbm7yreshuyl5i

General compact labeling schemes for dynamic trees

Amos Korman
2007 Distributed computing  
This paper investigates labeling schemes for dynamic trees.  ...  A general method for constructing labeling schemes for dynamic trees (under the above mentioned dynamic tree models) was previously developed in [29] .  ...  The label size of both schemes is O(log 2 n + log n log W ) where W denotes the largest edge weight in the tree.  ... 
doi:10.1007/s00446-007-0035-z fatcat:wvhz255tp5hsdadbkuna2wlw2m

Localized Network Representations [chapter]

David Peleg
2003 Lecture Notes in Computer Science  
reflect current situation Goal: localized labeling schemes using distributed adaptive marker protocols Result 1: ∃ distributed distance labeling scheme for dynamic trees using O(log 2 n) bit labels with  ...  min-weight subtree spanning W Steiner(W ) = its weight Steiner labeling scheme: deduces Steiner(W ) given labels {Label(v) | v ∈ W } T (n, µ) = class of n-node trees with µ-bit edge weights Thm: L(Steiner  ...  Adding v: ψ(u) increases by 1 ⇔ v ∈ subtree(w) for some w ∈ Common(u) ⇔ u is on path (  ... 
doi:10.1007/3-540-44849-7_1 fatcat:7algq4u67ba63om5a4vb43kmk4

An Experimental Analysis of Change Propagation in Dynamic Trees

Umut A. Acar, Guy E. Blelloch, Jorge L. Vittes
2005 Workshop on Algorithm Engineering and Experimentation  
As a second contribution, we present a library for dynamic-trees that support a general interface and present an experimental evaluation by considering a broad set of applications.  ...  The dynamic-trees library relies on change propagation to handle edge insertions/deletions.  ...  For applications, we assume that the edges and vertices of trees can be assigned weights (for edges) and labels (for vertices) respectively. Weights and labels can be of any type.  ... 
dblp:conf/alenex/AcarBV05 fatcat:eugj5wjqlfd7ljpvdtcqdhgb6m

Informative Labeling Schemes for Graphs [chapter]

David Peleg
2000 Lecture Notes in Computer Science  
We begin by developing f labeling schemes for three functions f over the class of n-vertex trees.  ...  Considering the class of n-vertex trees with M-bit edge weights, it is shown that for this class there exists a Steiner labeling scheme using O((M + log n) log n) bit labels, which is asymptotically optimal  ...  Acknowledgements I am grateful to Michal Katz and Nir Katz for their helpful comments and suggestions.  ... 
doi:10.1007/3-540-44612-5_53 fatcat:tr3wjlnap5azzmjazyv2x2dqpq

Informative labeling schemes for graphs

David Peleg
2005 Theoretical Computer Science  
We begin by developing f labeling schemes for three functions f over the class of n-vertex trees.  ...  Considering the class of n-vertex trees with M-bit edge weights, it is shown that for this class there exists a Steiner labeling scheme using O((M + log n) log n) bit labels, which is asymptotically optimal  ...  Acknowledgements I am grateful to Michal Katz and Nir Katz for their helpful comments and suggestions.  ... 
doi:10.1016/j.tcs.2005.03.015 fatcat:aigpwzyhorh3rpueyf4ita7iwu
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