PerturbationRank: A Non-monotone Ranking Algorithm

We introduce a new approach for ranking Web pages to capture the extent to which the whole Web depends on an individual Web page. The importance of a Web page is measured by how much the Web changes when the page is disconnected from the Web. While there are potentially many useful ways to quantify the change, in this work we focus on the following: represent the state of the Web by the output of a known ranking algorithm, and measure the change by an appropriate metric on the state space. More specifically, we present PerturbationRank, as we have termed our class of ranking algorithms, in combination with PageRank and HITS. While both base algorithms, together with several others, view an incoming link as a positive endorsement and are in essence methods to account for the total endorsement, PerturbationRank represents a fundamental departure from this paradigm. As a consequence, it is able to capture usefulness signals missed previously. We evaluate the performance of the new algorithms in comparison with the base algorithms, following the methodology of Borodin et al. (ACM Transactions on Internet Technology, 5(1), 231–297, 2005). Our experiments demonstrate that the new and the base rankings are considerably correlated, have comparable effectiveness, and are at the same time substantially different. We conclude that PerturbationRank algorithms give alternative and useful rankings of the Web. Finally, we discuss how to improve the computation efficiency of PerturbationRank, as well as its other potential applications such as in network security and in combating spamdexing.