We theoretically analyze the Cops and Robber Game for the first time in a multidimensional grid. It is shown that for an ndimensional grid, at least n cops are necessary to ensure capture of theâ€¦ (More)

We show that there exists a Boolean function F which observes the following separations among deterministic query complexity (D(F)), randomized zero error query complexity (R0(F)) and randomizedâ€¦ (More)

This paper focusses on the performance of the Metropolis algorithm when employed for solving combinatorial optimization problems. One finds in the literature two notions of success for the Metropolisâ€¦ (More)

We prove that the Fourier dimension of any Boolean function with Fourier sparsity s is at most O ( âˆš s log s). This bound is tight upto a factor of log s as the Fourier dimension and sparsity of theâ€¦ (More)

Let the randomized query complexity of a relation for error probability be denoted by R (Â·). We prove that for any relation f âŠ† {0, 1} Ã— R and Boolean function g : {0, 1} â†’ {0, 1}, R1/3(f â—¦g) =â€¦ (More)

The pointer function of GÃ¶Ã¶s, Pitassi and Watson [5] and its variants have recently been used to prove separation results among various measures of complexity such as deterministic, randomized andâ€¦ (More)

We initiate a systematic study of linear sketching over F2. For a given Boolean function treated as f : Fn 2 â†’ F2 a randomized F2-sketch is a distribution M over d Ã— n matrices with elements over F2â€¦ (More)