TAILIEUCHUNG - Data Structures on Event Graphs

This is the problem with benchmarking Security Information Event Management (SIEM) sys- tems, which collect security events from one to thousands of devices, each with its own differ- ent log data format. If we take every conceivable environment into consideration, it is impossi- ble to benchmark SIEM systems. We can, however, set one baseline environment against which to benchmark and then include equations so that organizations can extrapolate their own benchmark requirements. That is the approach of this paper | Data Structures on Event Graphs Bernard Chazelle1 and Wolfgang Mulzer2 1 Department of Computer Science Princeton University USA chazelle@ 2 Institut fur Informatik Freie Universitat Berlin Germany mulzer@ Abstract. We investigate the behavior of data structures when the input and operations are generated by an event graph. This model is inspired by the model of Markov chains. We are given a fixed graph G whose nodes are annotated with operations of the type insert delete and query. The algorithm responds to the requests as it encounters them during a adversarial or random walk in G. We study the limit behavior of such a walk and give an efficient algorithm for recognizing which structures can be generated. We also give a near-optimal algorithm for successor searching if the event graph is a cycle and the walk is adversarial. For a random walk the algorithm becomes optimal. 1 Introduction In contrast with the traditional adversarial assumption of worst-case analysis many data sources are modeled by Markov chains . in queuing speech gesture protein homology web searching etc. . These models are very appealing because they are widely applicable and simple to generate. Indeed locality of reference an essential pillar in the design of efficient computing systems is often captured by a Markov chain modeling the access distribution. Hence it does not come as a surprise that this connection has motivated and guided much of the research on self-organizing data structures and online algorithms in a Markov setting 1 7-11 15-18 . That body of work should be seen as part of a larger effort to understand algorithms that exploit the fact that input distributions often exhibit only a small amount of entropy. This effort is driven not only by the hope for improvements in practical applications . exploiting coherence in data streams but it is also motivated by theoretical questions for example the key to resolving the problem of designing an .

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