Bounds for products of interval functions

Improved Interval Bounds for Ranges of Functions

Compression bounds for wreath products

We show that if G and H are finitely generated groups whose Hilbert compression exponent is positive, then so is the Hilbert compression exponent of the wreath G ≀ H . We also prove an analogous result for coarse embeddings of wreath products. In the special case G = Z, H = Z ≀ Z our result implies that the Hilbert compression exponent of Z ≀ (Z ≀ Z) is at least 1/4, answering a question posed ...

Sharp Upper bounds for Multiplicative Version of Degree Distance and Multiplicative Version of Gutman Index of Some Products of Graphs

In $1994,$ degree distance  of a graph was introduced by Dobrynin, Kochetova and Gutman. And Gutman proposed the Gutman index of a graph in $1994.$ In this paper, we introduce the concepts of  multiplicative version of degree distance and the multiplicative version of Gutman index of a graph. We find the sharp upper bound for the  multiplicative version of degree distance and multiplicative ver...

Formulas for the width of interval products

Sharp formulas for the width of the product of intervals are derivedwhich are simpler ahd more effective :than the ones previously, known. These formulas are useful in applications and they are appropriate tools for estimating the' quality of interval evaluations, proofs of such formulas will, in general, result in a number of different cases involving' longwinded cak'ulations. By utilizing cer...

Bounds for Overlapping Interval Join on MapReduce

We consider the problem of 2-way interval join, where we want to find all pairs of overlapping intervals, i.e., intervals that share at least one point in common. We present lower and upper bounds on the replication rate for this problem when it is implemented in MapReduce. We study three cases, where intervals in the input are: (i) unit-length and equally-spaced, (ii) variable-length and equal...