Densest Subgraph in Dynamic Graph Streams

In this paper, we consider the problem of approximating the densest subgraph in the dynamic graph stream model. In this model of computation, the input graph is defined by an arbitrary sequence of edge insertions and deletions and the goal is to analyze properties of the resulting graph given memory that is sub-linear in the size of the stream. We present a single-pass algorithm that returns a $(1+\epsilon)$ approximation of the maximum density with high probability; the algorithm uses O(\epsilon^{-2} n \polylog n) space, processes each stream update in \polylog (n) time, and uses \poly(n) post-processing time where $n$ is the number of nodes. The space used by our algorithm matches the lower bound of Bahmani et al.~(PVLDB 2012) up to a poly-logarithmic factor for constant $\epsilon$. The best existing results for this problem were established recently by Bhattacharya et al.~(STOC 2015). They presented a $(2+\epsilon)$ approximation algorithm using similar space and another algorithm that both processed each update and maintained a $(4+\epsilon)$ approximation of the current maximum density in \polylog (n) time per-update.Comment: To appear in MFCS 201

The exponential time complexity of computing the probability that a graph is connected

We show that computation of all-terminal graph reliability requires time exponential in Ω(m/ log2 m) for simple graphs of m edges under the Exponential Time Hypothesis

Sex steroid binding proteins in the plasma of hatchling Chelonia mydas

Sex steroid binding proteins were identified in hatchling female and male Chelonia mydas by dialysis and steady-state gel electrophoresis when examined at 4 degrees C. A testosterone binding protein with high binding affinity (K (a) = 0.98 +/- 0.5 x 10(8) M(-1)) and low to moderate binding capacity (B (max) = 7.58 +/- 4.2 x 10(-5) M) was observed in male hatchlings. An oestradiol binding protein with high affinity (K (a) = 0.35 +/- 1.8 x 10(8) M(-1)) and low to moderate binding capacity (B (max) = 0.16 +/- 0.5 x 10(-4) M) was identified in female hatchlings. This study confirmed that sex steroid binding proteins (SSBPs) become inactivate in both sexes at 36 degrees C, the maximum body temperature of sea turtle hatchlings at emergence. The inactivation of SSBPs at this temperature indicates that sex steroid hormones circulate freely in the body of the green turtles and are biologically available in the blood plasma. This observation is consistent with female and male hatchling C. mydas having different physiological (hormonal) and developmental requirements around the time of emergence. Moreover, concurrently conducted competition studies showed that sex steroids including testosterone and oestradiol do compete for binding sites in both male and female C. mydas hatchling plasma. Competition also occurred between testosterone and dihydrotestosterone for binding sites in the male C. mydas plasma. However, competition studies in the plasma of female hatchling C. mydas demonstrate that oestrone does not compete with oestradiol for binding sites

Continuous query processing; Temporal analytics; Dynamic social

networks; Incremental computation