optimization - Algorithms for bucketizing integers into buckets with zero sums -

suppose have array of integers (both negative , positive) a[1 ... n] such elements sum zero. now, whenever have bunch of integers sum zero, call them group , want split a in many disjoint groups possible. can suggest paper discussing same problem?

it sounds problem consists of 2 np-complete problems.

the first finding subsets solve subset sum problem. problem have exponential time complexity (as implied amit in comments), reasonable extension of subset sum problem theoretical standpoint. example, if can solve subset sum problem dynamic programming , generate canonical 2d array result, array contain enough information generate possible solutions using traceback.

the second np-complete problem embedded within problem integer linear programming problem. given possible subsets solving subset sum problem, n total, want select select 0<=n<=n, such value of n maximized , no element of repeated.

i doubt there publication devoted describing problem because seems involve straightforward application of known theory.