Mustazee Rahman

activity

20112026

most citedLocal algorithms for independent sets are half-optimal

87 citations · 243 across the 20 of their papers we have counts for

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Showing 2014Show all

4 papers · 1 filter

math.PR2014★ 12 cited

Factor of iid percolation on trees

Mustazee Rahman

We study invariant percolation processes on the d-regular tree that are obtained as a factor of an iid process. We show that the density of any factor of iid site percolation proce…

math.CO2014

On variants of Conway and Conolly's Meta-Fibonacci recursions

Abraham Isgur, Mustazee Rahman

We study the recursions $A (n) = A (n - a - A^{k} (n - b)) + A (A^{k} (n - b))$ where $a \geq 0$ , $b \geq 1$ are integers and the superscript $k$ denotes a $k$ -fold composition, and also the recurs…

math.PR2014★ 2 cited

Percolation with small clusters on random graphs

Mustazee Rahman

Consider the problem of determining the maximal induced subgraph in a random $d$ -regular graph such that its components remain bounded as the size of the graph becomes arbitrarily…

math.PR2014★ 87 cited

Local algorithms for independent sets are half-optimal

Mustazee Rahman, Balint Virag

We show that the largest density of factor of i.i.d. independent sets on the d-regular tree is asymptotically at most (log d)/d as d tends to infinity. This matches the lower bound…