The subgraph homeomorphism problem

AbstractWe investigate the problem of finding a homeomorphic image of a “pattern” graph H in a larger input graph G. We view this problem as finding specified sets of edge disjoint or node disjoint paths in G. Our main result is a linear time algorithm to determine if there exists a simple cycle containing three given nodes in G (here H is a triangle). No polynomial time algorithm for this problem was previously known. We also discuss a variety of reductions between related versions of this problem and a number of open problems

Enabling Author-Centric Ranking of Web Content

In the past decade there has been a rapid increase in the amount of web content, partially due to wide-spread adoption of blogging and micro-blogging platforms that make it easy for ordinary users to quickly create web content. A single user may create content on many different online platforms or social networks. Current web search systems largely rely on link-structure of the web graph in ranking content. In other words, they care about “who links to a webpage ” and are largely agnostic to “who authored the content on this webpage”. In this paper, we argue that in addition to link-structure the topic-authority of the original author can provide important signals for ranking and discovery of web content. We present algorithms for transferring topic-authority between webpages based on a same-origin policy. Our preliminary results suggest that such topicauthority transfers can improve the visibility of certain types of content compared to a link-structure only approach