# Sorting sums of binary decision summands

## TL;DR

This paper presents an efficient algorithm with quadratic complexity for finding the top K smallest or largest sums from a set of binary decision summands, avoiding exhaustive enumeration.

## Contribution

It introduces an $ ext{O}(K^2)$ algorithm to efficiently identify extremal sums among exponentially many possibilities.

## Key findings

- The algorithm efficiently computes top sums without enumerating all possibilities.
- It significantly reduces computational complexity for large N and K.
- The method is applicable to problems involving binary decision sums.

## Abstract

A sum where each of the $N$ summands can be independently chosen from two choices yields $2^N$ possible summation outcomes. There is an $\mathcal{O}(K^2)$-algorithm that finds the $K$ smallest/largest of these sums by evading the enumeration of all sums.