TY - GEN

T1 - Optimal gradient clock synchronization in dynamic networks

AU - Kuhn, Fabian

AU - Lenzen, Christoph

AU - Locher, Thomas

AU - Oshman, Rotem

PY - 2010

Y1 - 2010

N2 - We study the problem of clock synchronization in highly dynamic networks, where communication links can appear or disappear at any time. The nodes in the network are equipped with hardware clocks, but the rate of the hardware clocks can vary arbitrarily within specific bounds, and the estimates that nodes can obtain about the clock values of other nodes are inherently inaccurate. Our goal in this setting is to output a logical clock at each node, such that the logical clocks of any two nodes are not too far apart, and nodes that remain close to each other in the network for a long time are better synchronized than distant nodes. This property is called gradient clock synchronization. Gradient clock synchronization has been widely studied in the static setting. We show that the bounds for the static case also apply to our highly dynamic setting: if two nodes remain at distance d from each other for sufficiently long, it is possible to synchronize their clocks to within O(d log(D/d)), where D is the diameter of the network. This is known to be optimal for static networks, and since a static network is a special case of a dynamic network, it is optimal for dynamic networks as well. Furthermore, we show that our algorithm has optimal stabilization time: when a path of length d appears between two nodes, the time required until the skew between the two nodes is reduced to O(d log(D/d)) is O(D), which we prove is optimal.

AB - We study the problem of clock synchronization in highly dynamic networks, where communication links can appear or disappear at any time. The nodes in the network are equipped with hardware clocks, but the rate of the hardware clocks can vary arbitrarily within specific bounds, and the estimates that nodes can obtain about the clock values of other nodes are inherently inaccurate. Our goal in this setting is to output a logical clock at each node, such that the logical clocks of any two nodes are not too far apart, and nodes that remain close to each other in the network for a long time are better synchronized than distant nodes. This property is called gradient clock synchronization. Gradient clock synchronization has been widely studied in the static setting. We show that the bounds for the static case also apply to our highly dynamic setting: if two nodes remain at distance d from each other for sufficiently long, it is possible to synchronize their clocks to within O(d log(D/d)), where D is the diameter of the network. This is known to be optimal for static networks, and since a static network is a special case of a dynamic network, it is optimal for dynamic networks as well. Furthermore, we show that our algorithm has optimal stabilization time: when a path of length d appears between two nodes, the time required until the skew between the two nodes is reduced to O(d log(D/d)) is O(D), which we prove is optimal.

KW - Clock synchronization

KW - Dynamic networks

UR - http://www.scopus.com/inward/record.url?scp=77956246759&partnerID=8YFLogxK

U2 - 10.1145/1835698.1835799

DO - 10.1145/1835698.1835799

M3 - פרסום בספר כנס

AN - SCOPUS:77956246759

SN - 9781605588889

T3 - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

SP - 430

EP - 439

BT - PODC'10 - Proceedings of the 2010 ACM Symposium on Principles of Distributed Computing

Y2 - 25 July 2010 through 28 July 2010

ER -