Find the minimum possible difference between two arrays

I'll implement Shridhar's suggestion of identifying the best modification for each element individually in O(n log n) time and taking the best one.

import bisect

def abs_diff(x, y):
    return abs(x - y)

def find_nearest(sorted_a, y):
    i = bisect.bisect(sorted_a, y)
    return min(
        sorted_a[max(i - 1, 0) : min(i + 1, len(sorted_a))],
        key=lambda z: abs_diff(z, y),

def improvement(x, y, z):
    return abs_diff(x, y) - abs_diff(z, y)

def min_diff(a, b):
    sorted_a = sorted(a)
    nearest = [find_nearest(sorted_a, y) for y in b]
    return sum(map(abs_diff, a, b)) - max(map(improvement, a, b, nearest))

print(min_diff([1, 3, 5], [5, 3, 1]))