How to be an efficient snoop, or the probe complexity of quorum systems (extended abstract)
PODC '96 Proceedings of the fifteenth annual ACM symposium on Principles of distributed computing
Improving the Availability of Mutual Exclusion Systems on Incomplete Networks
IEEE Transactions on Computers
Average probe complexity in quorum systems
Proceedings of the twentieth annual ACM symposium on Principles of distributed computing
Quorum systems constructed from combinatorial designs
Information and Computation
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Average probe complexity in quorum systems
Journal of Computer and System Sciences
Distributed Computing - Special issue: PODC 04
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This paper introduces and studies the question of balancing the load on processors participating in a given quorum system. Our proposed measure for the degree of balancing is the ratio between the load on the least frequently referenced element and on the most frequently used one.We give some simple sufficient and necessary conditions for perfect balancing. We then look at the balancing properties of the common class of voting systems and prove that every voting system with odd total weight is perfectly balanced. (This holds, in fact, for the more general class of ordered systems.)We also give some characterizations for the balancing ratio in the worst case. It is shown that for any quorum system with a universe of size $n$, the balancing ratio is no smaller than $1/(n-1)$, and this bound is the best possible. When restricting attention to nondominated coteries (NDCs), the bound becomes $2/\bigl(n-\log_2 n+o(\log n)\bigr)$, and there exists an NDC with ratio $2/\bigl(n-\log_2 n-o(\log n)\bigr)$.Next, we study the interrelations between the two basic parameters of load balancing and quorum size. It turns out that the two size parameters suitable for our investigation are the size of the largest quorum and the optimally weighted average quorum size(OWAQS) of the system. For the class of ordered NDCs (for which perfect balancing is guaranteed), it is shown that over a universe of size $n$, some quorums of size $\lceil(n+1)/2\rceil$ or more must exist (and this bound is the best possible). A similar lower bound holds for the OWAQS measure if we restrict attention to voting systems. For nonordered systems, perfect balancing can sometimes be achieved with much smaller quorums. A lower bound of $\Omega(\sqrt{n})$ is established for the maximal quorum size and the OWAQS of any perfectly balanced quorum system over $n$ elements, and this bound is the best possible.Finally, we turn to quorum systems that cannot be perfectly balanced, but have some balancing ratio $0