In this paper, we study the approximability of the metric Traveling Salesman Problem, one of the most widely studied problems in combinatorial optimization. Currently, the best known hardness of approximation bounds are 185/184 for the symmetric case (due to Lampis) and 117/116 for the asymmetric case (due to Papadimitriou and ... more >>>

We study shared randomness in the context of multi-party number-in-hand communication protocols in the simultaneous message passing model. We show that with three or more players, shared randomness exhibits new interesting properties that have no direct analogues in the two-party case.

First, we demonstrate a hierarchy of modes of shared ... more >>>

We propose that multi-linear functions of relatively low degree
over GF(2) may be good candidates for obtaining exponential
lower bounds on the size of constant-depth Boolean circuits
(computing explicit functions).
Specifically, we propose to move gradually from linear functions
to multilinear ones, and conjecture that, for any $t\geq2$,
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