Ranking Information in Networks

Given an information network, we are interested in ranking sets of nodes that score highest on user-specified criteria. Examples include (1) discovering sets of authors with expertise in a wide range of disciplines; (2) finding sets of patents which, if removed, would have the greatest effect on the patent citation network; (3) identifying small sets of IP addresses which taken together account for a significant portion of a typical day’s traffic; and (4) detecting sets of countries whose vote agree with a given country (e.g., USA) on a wide range of UN resolutions. We present this ranking task as a Top-K problem. We assume the criteria is defined by L real-valued features on nodes. This gives us a matrix F , whose rows represent the N nodes and whose columns represent the L real-valued features. Examples of these node-centric features include degree, betweenness, PageRank, etc. We define an L-tuple �v1, . . . , vL� as a selection of one value from each column. The score of an L-tuple is equal to the sum of the selected values (i.e., sum of the tuple’s components). For a given parameter K, we require an algorithm that efficiently lists the top K L-tuples ordered from best (highest score) to worst. The L-tuple with the highest score corresponds to a set of nodes in which all features take on optimal values. As described in the next section, we solve the Top-K problem by utilizing SMA* [1], which is a fixedmemory heuristic search algorithm. SMA* requires the specification of an additional parameter M for the maximum allotted memory-size. The choice for M has a dramatic effect on runtime. To solve this inefficiency problem, we introduce a parallelization of SMA* (on distributed-memory machines) that increases the effective memory size and produces super-linear speedups. This allows use to efficiently solve the Top-K ranking problem for large L and K (e.g., L ∈ [102, 103] and K ∈ [106, 109]). Experiments on synthetic and real data illustrate the effectiveness of our solution.