Fillable arrays with constant time operations and a single bit of redundancy

In the fillable array problem one must maintain an array A[1..n] of w-bit entries subject to random access reads and writes, and also a fill(∆) operation which sets every entry of A to some ∆ ∈ {0, . . . , 2− 1}. We show that with just one bit of redundancy, i.e. a data structure using nw + 1 bits of memory, read/fill can be implemented in worst case constant time, and write can be implemented in either amortized constant time (deterministically) or worst case expected constant (randomized). In the latter case, we need to store an additional O(lgn) random bits to specify a permutation drawn from an 1/nalmost pairwise independent family.