Cheaper Matrix Clocks

abstract : Matrix clocks have nice properties that can be used in the context of distributed database protocols and fault tolerant protocols. Unfortunately, they are costly to implement, requiring storage and communication overhead of size O(n 2) for a system of n sites. They are often considered a non feasible approach when the number of sites is large. In this paper, we rstly describe an eecient incremental algorithm to compute the matrix clock, which achieves storage and communication overhead of size O(n) when the sites of the computation are \well syn-chronized". Secondly, we introduce the k-matrix clock: an approximation to the genuine matrix clock that can be computed with a storage and communication overhead of size O(kn). k-matrix clocks can be useful to implement fault-tolerant protocols for systems with crash failure semantics such that the maximum number of simultaneous faults is bounded by k ? 1. Abstract Matrix clocks have nice properties that can be used in the context of distributed database protocols and fault tolerant protocols. Unfortunately, they are costly to implement, requiring storage and communication overhead of size O(n 2) for a system of n sites. They are often considered a non feasible approach when the number of sites is large. In this paper, we rstly describe an eecient incremental algorithm to compute the matrix clock, which achieves storage and communication overhead of size O(n) when the sites of the computation are \well synchronized". Secondly, we introduce the k-matrix clock: an approximation to the genuine matrix clock that can be computed with a storage and communication overhead of size O(kn). k-matrix clocks can be useful to implement fault-tolerant protocols for systems with crash failure semantics such that the maximum number of simultaneous faults is bounded by k ? 1.