We study a new model of computation, called best-order stream, for graph problems. Roughly, it is a proof system where a space-limited verifier has to verify a proof sequentially (i.e., it reads the proof as a stream). Moreover, the proof itself is just a specific ordering of the input data.

This model is closely related to many models of computation in other areas such as data streams, communication complexity, and proof checking, and could be used in applications such as cloud computing.

In this paper we focus on graph problems where the input is a sequence of edges. We show that even under this model, checking some basic graph properties deterministically requires linear space in the number of nodes. We also show that, in contrast with this, randomized verifiers are powerful enough to check many graph properties in polylogarithmic space.

## Another publication from the same category: Machine Learning and Data Science

### Drawing Sound Conclusions from Noisy Judgments

The quality of a search engine is typically evaluated using hand-labeled data sets, where the labels indicate the relevance of documents to queries. Often the number of labels needed is too large to be created by the best annotators, and so less accurate labels (e.g. from crowdsourcing) must be used. This introduces errors in the labels, and thus errors in standard precision metrics (such as P@k and DCG); the lower the quality of the judge, the more errorful the labels, consequently the more inaccurate the metric. We introduce equations and algorithms that can adjust the metrics to the values they would have had if there were no annotation errors.

This is especially important when two search engines are compared by comparing their metrics. We give examples where one engine appeared to be statistically significantly better than the other, but the effect disappeared after the metrics were corrected for annotation error. In other words the evidence supporting a statistical difference was illusory, and caused by a failure to account for annotation error.

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