TY - GEN

T1 - Local-on-average distributed tasks

AU - Parter, Merav

AU - Peleg, David

AU - Solomon, Shay

PY - 2016

Y1 - 2016

N2 - A distributed task is local if its time complexity is (nearly) constant, otherwise it is global. Unfortunately, local tasks are relatively scarce, and most distributed tasks require time at least logarithmic in the network size (and often higher than that). In a dynamic setting, i.e., when the network undergoes repeated and frequent topological changes, such as vertex and edge insertions and deletions, it is desirable to be able to perform a local update procedure around the modified part of the network, rather than running a static global algorithm from scratch following each change. This paper makes a step towards establishing the hypothesis that many (statically) non-local distributed tasks are local-on-average in the dynamic setting, namely, their amortized time complexity is O(log∗ n). Towards establishing the plausibility of this hypothesis, we propose a strategy for transforming static O(polylog(n)) time algorithms into dynamic O(log∗ n) amortized time update procedures. We then demonstrate the usefulness of our strategy by applying it to several fundamental problems whose static time complexity is logarithmic, including forestdecomposition, edge-orientation and coloring sparse graphs, and show that their amortized time complexity in the dynamic setting is indeed O(log∗ n).

AB - A distributed task is local if its time complexity is (nearly) constant, otherwise it is global. Unfortunately, local tasks are relatively scarce, and most distributed tasks require time at least logarithmic in the network size (and often higher than that). In a dynamic setting, i.e., when the network undergoes repeated and frequent topological changes, such as vertex and edge insertions and deletions, it is desirable to be able to perform a local update procedure around the modified part of the network, rather than running a static global algorithm from scratch following each change. This paper makes a step towards establishing the hypothesis that many (statically) non-local distributed tasks are local-on-average in the dynamic setting, namely, their amortized time complexity is O(log∗ n). Towards establishing the plausibility of this hypothesis, we propose a strategy for transforming static O(polylog(n)) time algorithms into dynamic O(log∗ n) amortized time update procedures. We then demonstrate the usefulness of our strategy by applying it to several fundamental problems whose static time complexity is logarithmic, including forestdecomposition, edge-orientation and coloring sparse graphs, and show that their amortized time complexity in the dynamic setting is indeed O(log∗ n).

UR - http://www.scopus.com/inward/record.url?scp=84962855633&partnerID=8YFLogxK

U2 - 10.1137/1.9781611974331.ch17

DO - 10.1137/1.9781611974331.ch17

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AN - SCOPUS:84962855633

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 220

EP - 239

BT - 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016

A2 - Krauthgamer, Robert

PB - Association for Computing Machinery

T2 - 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016

Y2 - 10 January 2016 through 12 January 2016

ER -