Strongly Polynomial Deterministic Algorithm for DisProdTV

Determine whether a strongly polynomial deterministic algorithm exists for DisProdTV, the problem of approximating the total variation distance between two product distributions over a finite domain [M]^n to within a specified relative error, where the number of arithmetic operations is bounded by a polynomial in n, M, and 1/epsilon independent of the bit-length of the input parameters.

Background

The paper reviews deterministic and randomized polynomial-time algorithms for DisProdTV (approximating TV distance between products of discrete distributions) and discusses bit-complexity considerations. While these algorithms run in polynomial time in terms of bit complexity, the deterministic algorithm's arithmetic operation count depends on the input representation length, and thus is not strongly polynomial.

The authors explicitly note the absence of a known strongly polynomial deterministic algorithm for DisProdTV, highlighting a gap between current results and a stronger complexity guarantee where the arithmetic operation count depends only on structural parameters (n, M, 1/epsilon).