 
Summary: A Modular Measure of Competitiveness for Distributed Algorithms
James Aspnes Orli Waartsy
The tool of competitive analysis has long been used to
deal with nondeterminism in the form of unpredictable re
quest sequences in online settings. The performance mea
sure of an algorithm is its competitive ratio, the supremum
over all possible request sequences of the ratio of the algo
rithm's cost to the cost of an optimal algorithm. This mea
sure is often more practical than worstcase analysis, since it
measures the ability of an algorithm to adapt to easy inputs
as well as its ability to tolerate di cult ones.
In an asynchronous distributed setting, in addition to the
unknown input (the sequence of future user requests), there
is the unknown schedule (the timing of events in the system
such as the arrival of messages in a messagepassing model or
the completion of lowlevel operations in a sharedmemory
model). Much of the work that has applied competitive
analysis to distributed problems has the online and opti
mal algorithms compete only on the same input, generally
hiding the details of the schedule in a worstcase assump
