Enumerative combinatorics
Efficient management of transitive relationships in large data and knowledge bases
SIGMOD '89 Proceedings of the 1989 ACM SIGMOD international conference on Management of data
Partial orders for parallel debugging
PADD '88 Proceedings of the 1988 ACM SIGPLAN and SIGOPS workshop on Parallel and distributed debugging
Concerning the size of logical clocks in distributed systems
Information Processing Letters
Efficient handling of multiple inheritance hierarchies
OOPSLA '93 Proceedings of the eighth annual conference on Object-oriented programming systems, languages, and applications
Time, clocks, and the ordering of events in a distributed system
Communications of the ACM
Exploiting the Induced Order on Type-Labeled Graphs for Fast Knowledge Retrieval
ICCS '94 Proceedings of the Second International Conference on Conceptual Structures: Current Practices
ACM SIGACT News distributed computing column 12
ACM SIGACT News
Efficient dependency tracking for relevant events in shared-memory systems
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Efficient dependency tracking for relevant events in concurrent systems
Distributed Computing
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In this paper, we show the connection between vector clocks used in distributed computing and dimension theory of partially ordered sets. Based on this connection, we provide lower bounds on the number of coordinates for timestamping events in a distributed computation for capturing the happened- before relation. To this end, we introduce the notion of a string realizer and the string dimension of a poset. For distributed computing and other applications, the concept of string realizer is more natural than the chain realizer used in the classical dimension theory. We establish the relationship between the string dimension and the chain dimension of a poset. Using this relationship and Dilworth's theorem for the chain dimension of finite distributive lattices, we obtain the desired lower bound. The concept of strings also has applications in efficient encoding of partial orders because it requires fewer bits to encode a string realizer than a chain realizer.