We describe an approach for incorporating randomization in the teaching of data structures and algorithms. The proofs we include are quite simple and can easily be made a part of a Freshman-Sophomore Introduction to Data Structures (CS2) course and a Junior-Senior level course on the design and analysis of data structures and algorithms (CS7/DS&A). The main idea of this approach is to show that using randomization in data structures and algorithms is safe and can be used to significantly simplify efficient solutions to various computational problems. We illustrate this approach by giving examples of the use of randomization in some traditional topics from CS2 and DS&A.

Using randomization in the teaching of data structures and algorithms

Skip graphs are a novel distributed data structure, based on skip lists, that provide the full functionality of a balanced tree in a distributed system where resources are stored in separate nodes that may fail at any time. They are designed for use in searching peer-to-peer systems, and by providing the ability to perform queries based on key ordering, they improve on existing search tools that provide only hash table functionality. Unlike skip lists or other tree data structures, skip graphs are highly resilient, tolerating a large fraction of failed nodes without losing connectivity. In addition, simple and straightforward algorithms can be used to construct a skip graph, insert new nodes into it, search it, and detect and repair errors within it introduced due to node failures.

Skip graphs

The path length of random skip lists

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The path length of random skip lists