Incremental Maintenance of Maximal Cliques in a Dynamic Graph

We consider the maintenance of the set of all maximal cliques in a dynamic graph that is changing through the addition or deletion of edges. We present nearly tight bounds on the magnitude of change in the set of maximal cliques, as well as the first change-sensitive algorithms for clique maintenance, whose runtime is proportional to the magnitude of the change in the set of maximal cliques. We present experimental results showing these algorithms are efficient in practice and are faster than prior work by two to three orders of magnitude.Comment: 18 pages, 8 figure

Mining maximal cliques from large graphs using MapReduce

Maximal clique enumeration (MCE), a fundamental task in graph analysis, can help identify dense substructures within a graph, and has found applications in graphs arising in biological and chemical networks, and more. While MCE is well studied in the sequential case, a single machine can no longer process large graphs arising in today\u27s applications, and effective ways are needed for processing these in parallel. This work introduces PECO (Parallel Enumeration of Cliques using Ordering); a novel parallel MCE algorithm. Unlike previous works, which require a post-processing step to remove duplicate and non-maximal cliques, PECO enumerates maximal cliques with no duplicates while minimizing work redundancy and eliminating the need for an additional post-processing step. This is achieved by dividing the input graph into smaller overlapping subgraphs, and by inducing a total ordering among the vertices. Then, as a subgraph is processed, the ordering is used in tandem with a sequential MCE algorithm to reduce redundant work while only enumerating a clique if it satisfies a certain condition with respect to the ordering, ensuring that each maximal clique is output exactly once. It is well recognized that in enumerating maximal cliques, the sizes of different subproblems can be non-uniform, and load balancing among the subproblems is a significant issue. Our algorithm uses the above vertex ordering to greatly improve load balancing when compared with straightforward approaches to parallelization. PECO has been designed and implemented for the MapReduce framework, but this technique is applicable to other parallel frameworks as well. Our experiments on a variety of large real world graphs, using several ordering strategies, show that PECO can enumerate cliques in large graphs of well over a million vertices and tens of millions of edges, and that it scales well to at least 64 processors. A comparison of ordering strategies shows that an ordering based on vertex degree performs the best, improving load balance and reducing total work when compared to the other strategies

Influence of Prolonged Exercise and Hydration Status on Antigen-Stimulated Cytokine Production by Whole Blood Culture

Prolonged, strenuous exercise has been associated with a temporal depression of host defence, increasing susceptibility to upper respiratory tract illness (URTI). An elevated anti-inflammatory cytokine response to antigen challenge at rest has been reported as a risk factor for URTI. Chronic, strenuous exercise training appears to augment this anti-inflammatory response, with IL-10 release predicting URTI susceptibility in athletes. The purpose of this study was to determine the acute effects of a bout of prolonged exercise and hydration status on antigen-stimulated cytokine production. Twelve healthy males cycled for 120 minutes at 60% of maximal oxygen uptake on two occasions, once in a euhydrated state and once moderately hypohydrated. For the euhydrated trial, participants drank ad libitum during the 24 hours prior to the trial, and were provided with 250 mL water every 30 minutes during exercise. For the hypohydrated trial, fluid intake was restricted to 500 mL water during the 24 hours leading up to the trial, and no fluid was ingested during exercise. Blood samples were collected immediately before and after exercise, and following 2 hours of passive recovery. A full blood count was obtained, and plasma analysed for cortisol. In vitro antigen-stimulated cytokine production was determined from whole blood culture, using a multi-antigen vaccine as stimulant. Fluid restriction resulted in body mass loss of 1.3 ± 0.7 % and 3.9 ± 1.0 % before and after exercise, respectively. Exercise elicited a significant leukocytosis and elevated plasma cortisol, with no differences between trials. Post-exercise IL-10 production following stimulation was significantly higher than pre-exercise (p\u3c0.01). Both IL-4 (p\u3c0.05) and IL-10 (p\u3c0.01) release per lymphocyte were significantly increased 2 hours post-exercise compared with pre-exercise. Antigen-stimulated IL-6 production was significantly reduced 2 hours post-exercise (p\u3c0.05), an effect that remained significant when expressed per monocyte (p\u3c0.01). Although not quite reaching statistical significance, antigen-stimulated IFN-γ and IL-8 release tended to decrease following exercise, as did monocyte production of TNF-α. IL-1β and IL-2 production were not significantly altered by exercise. No significant effect of hydration status was observed for any of the measured variables. Prolonged exercise appears to result in augmented anti-inflammatory cytokine release in response to antigen challenge, possibly coupled with an acute suppression of pro-inflammatory cytokine production. These findings correspond with previous studies using mitogen or endotoxin as stimulant. Neither cytokine production nor plasma cortisol was affected by moderate hypohydration induced by fluid restriction for 24 hours prior to and during exercise