Ergodic Control and Polyhedral approaches to PageRank Optimization by Olivier Fercoq, Marianne Akian, Mustapha Bouhtou, Stéphane Gaubert (Submitted on 10 Nov 2010 (v1), last revised 19 Sep 2011 (this version, v2))
Abstract:
We study a general class of PageRank optimization problems which consist in finding an optimal outlink strategy for a web site subject to design constraints. We consider both a continuous problem, in which one can choose the intensity of a link, and a discrete one, in which in each page, there are obligatory links, facultative links and forbidden links. We show that the continuous problem, as well as its discrete variant when there are no constraints coupling different pages, can both be modeled by constrained Markov decision processes with ergodic reward, in which the webmaster determines the transition probabilities of websurfers. Although the number of actions turns out to be exponential, we show that an associated polytope of transition measures has a concise representation, from which we deduce that the continuous problem is solvable in polynomial time, and that the same is true for the discrete problem when there are no coupling constraints. We also provide efficient algorithms, adapted to very large networks. Then, we investigate the qualitative features of optimal outlink strategies, and identify in particular assumptions under which there exists a “master” page to which all controlled pages should point. We report numerical results on fragments of the real web graph.
I mention this research to raise several questions:
- Does PageRank have a role to play in presentation for topic map systems?
- Should PageRank results in topic map systems be used assign subject identifications?
- If your answer to #2 is yes, what sort of subjects and how would you design the user choices leading to them?
- Are you monitoring user navigations of your topic maps?
- Has user navigation of your topic maps affected their revision or design of following maps?
- Are the navigations in #5 the same as choices based on search results? (In theory or practice.)
- Is there an optimal strategy for linking nodes in a topic map?