We improve on random sampling techniques for approximately solving problems that involve cuts in graphs. We give a lineartime construction that transforms any graph on n vertices into an O(n log n)-edge graph on the same vertices whose cuts have approximately the same value as the original graph's. In this new graph, for example, we can run theÕ(mn)-time maximum flow algorithm of Goldberg and Tarjan to find an s-t minimum cut inÕ(n 2 ) time. This corresponds to a (1 + )-times minimum s-t cut in the original graph. In a similar way, we can approximate a sparsest cut inÕ(n 2 ) time.

David Karger wishes to dedicate this work to the memory of Rajeev Motwani. His compelling teaching and supportive advising inspired and enabled the line of research [17,24,18,21] that led to the results published here.Abstract. We describe random sampling techniques for approximately solving problems that involve cuts and flows in graphs. We give a near-linear-time randomized combinatorial construction that transforms any graph on n vertices into an O(n log n)-edge graph on the same vertices whose cuts have approximately the same value as the original graph's. In this new graph, for example, we can run theÕ(m 3/2 )-time maximum flow algorithm of Goldberg and Rao to find an s-t minimum cut inÕ(n 3/2 ) time. This corresponds to a (1 + )-times minimum s-t cut in the original graph. A related approach leads to a randomized divide-and-conquer algorithm producing an approximately maximum flow inÕ(m √ n) time. Our algorithm can also be used to improve the running time of sparsest cut approximation algorithms fromÕ(mn) toÕ(n 2 ) and to accelerate several other recent cut and flow algorithms. Our algorithms are based on a general theorem analyzing the concentration of random graphs' cut values near their expectations. Our work draws only on elementary probability and graph theory.1. Introduction. This paper gives results on random sampling methods for reducing the number of edges in any undirected graph while approximately preserving the values of its cuts and consequently its flows. It then demonstrates how these techniques can be used in faster algorithms to approximate the values of minimum cuts and maximum flows in such graphs. We give anÕ(m)-time 1 compression algorithm to reduce the number of edges in any n-vertex graph to O(n log n) with only a small perturbation in cut values and then use that compression method to find approximate minimum cuts inÕ(n 2 ) time and approximate maximum flows inÕ(m √ n) time.

Ageing has a huge impact on human health and economy, but its molecular basis – regulation and mechanism – is still poorly understood. By today, more than three hundred genes (almost all of them function as protein-coding genes) have been related to human ageing. Although individual ageing-related genes or some small subsets of these genes have been intensively studied, their analysis as a whole has been highly limited. To fill this gap, for each human protein we extracted 21000 protein features from various databases, and using these data as an input to state-of-the-art machine learning methods, we classified human proteins as ageing-related or non-ageing-related. We found a simple classification model based on only 36 protein features, such as the “number of ageing-related interaction partners”, “response to oxidative stress”, “damaged DNA binding”, “rhythmic process” and “extracellular region”. Predicted values of the model quantify the relevance of a given protein in the regulation or mechanisms of the human ageing process. Furthermore, we identified new candidate proteins having strong computational evidence of their important role in ageing. Some of them, like Cytochrome b-245 light chain (CY24A) and Endoribonuclease ZC3H12A (ZC12A) have no previous ageing-associated annotations.

In this paper we give methods for time-aware music recommendation in a social media service with the potential of exploiting immediate temporal influences between users. We consider events when a user listens to an artist the first time and this event follows some friend listening to the same artist short time before. We train a blend of matrix factorization methods that model the relation of the influencer, the influenced and the artist, both the individual factor decompositions and their weight learned by variants of stochastic gradient descent (SGD). Special care is taken since events of influence form a subset of the positive implicit feedback data and hence we have to cope with two different definitions of the positive and negative implicit training data. In addition, in the time-aware setting we have to use online learning and evaluation methods. While SGD can easily be trained online, evaluation is cumbersome by traditional measures since we will have potentially different top recommendations at different times. Our experiments are carried over the two-year "scrobble" history of 70,000 Last.fm users and show a 5% increase in recommendation quality by predicting temporal influences.