Vladimir Ufimtsev

An extremely fast algorithm for identifying high closeness centrality vertices in large-scale networks

The significance of an entity in a network is generally given by the centrality value of its vertex. For most analysis purposes, only the high ranked vertices are required. However, most algorithms calculate the centrality values of all the vertices. We present an extremely fast and scalable algorithm for identifying the high closeness centrality vertices, using group testing. We show that our approach is significantly faster (best-case over 50 times, worst-case over 7 times) than the currently used methods. We can also use group testing to identify networks that are sensitive to edge perturbation.

Hypothesis group testing for disjoint pairs

Abstract Classical group testing (CGT) is a widely applicable biotechnical technique used to identify a small number of distinguished objects from a population when the presence of any one of these distinguished objects among a group of others produces an observable result. This paper discusses a variant of CGT called group testing for disjoint pairs (GTAP). The difference between the two is that in GTDP, the distinguished items are pairs from, not individual objects in, the population. There are several biological examples of when this abstract model applies. One biological example is DNA hybridization. The presence of pairs of hybridized DNA strands can be detected in a pool of DNA strands. Another situation is the detection of binding interactions between prey and bait proteins. This paper gives a random pooling method, similar in spirit to hypothesis testing, which identifies pairs of objects from a population that collectively have an observable function. This method is simply to apply, achieves good results, is amenable to automation and can be easily modified to compensate for testing errors.

DNA codes based on stem similarities between DNA sequences

DNA codes consisting of DNA sequences are necessary for DNA computing. The minimum distance parameter of such codes is a measure of how dissimilar the codewords are, and thus is indirectly a measure of the likelihood of undetectedable or uncorrectable errors occurring during hybridization. To compute distance, an abstract metric, for example, longest common subsequence, must be used to model the actual bonding energies of DNA strands. In this paper we continue the development [1,2,3] of similarity functions for q-ary n-sequences The theoretical lower bound on the maximal possible size of codes, built on the space endowed with this metric, is obtained. that can be used (for q = 4) to model a thermodynamic similarity on DNA sequences. We introduce the concept of a stem similarity function and discuss DNA codes [2] based on the stem similarity. We suggest an optimal construction [2] and obtain random coding bounds on the maximum size and rate for such codes.

Understanding Stability of Noisy Networks through Centrality Measures and Local Connections

Networks created from real-world data contain some inaccuracies or noise, manifested as small changes in the network structure. An important question is whether these small changes can signficantly affect the analysis results. In this paper, we study the effect of noise in changing ranks of the high centrality vertices. We compare, using the Jaccard Index (JI), how many of the top-k high centrality nodes from the original network are also part of the top-k ranked nodes from the noisy network. We deem a network as stable if the JI value is high. We observe two features that affect the stability. First, the stability is dependent on the number of top-ranked vertices considered. When the vertices are ordered according to their centrality values, they group into clusters. Perturbations to the network can change the relative ranking within the cluster, but vertices rarely move from one cluster to another. Second, the stability is dependent on the local connections of the high ranking vertices. The network is highly stable if the high ranking vertices are connected to each other. Our findings show that the stability of a network is affected by the local properties of high centrality vertices, rather than the global properties of the entire network. Based on these local properties we can identify the stability of a network, without explicitly applying a noise model.

ACM SRC poster: a scalable group testing based algorithm for finding d-highest betweenness centrality vertices in large scale networks

We present a group testing approach to identify the first d vertices with the highest betweenness centrality. Betweenness centrality (BC) of a vertex is the ratio of shortest paths that pass through it and is an important metric in complex networks. The Brandes algorithm computes the BC cumulatively over all vertices. Approximate BC of a single vertex can be computed by selective vertex sampling. However, applications such as community detection require only the vertices with the first few highest BC values, which are not known a-priori. In our method we sample a set of vertices and compute their combined BC. It can be shown that for small values of d, the number of tests required to find the d-highest BC vertices is logarithmic in the total number of vertices. Our algorithm is highly scalable since the samples are independently selected and therefore each test can be performed in parallel.

Building blocks for graph based network analysis

Network analysis using graph abstractions is a powerful tool for studying complex systems. While there are multiple libraries for both graph operations in general and network analysis algorithms in particular, there is no components based standardization of both of these key set of operations. We propose a framework that abstracts the data stuctures, architecture, programming models for the graph algorithms underneath a very simple component based interface. We also build on these graph abstractions to provide a layer of abstraction that are key for network analysis. A reference implementation of the abstractions and its performance is also demonstrated using a new library - ESSENS.