# Randomized Quasi Polynomial Algorithm for Subset-Sum Problems with At Most One Solution

In this paper we study the Subset Sum Problem (SSP). Assuming the SSP has at most one solution, we provide a randomized quasi-polynomial algorithm which if the SSP has no solution, the algorithm always returns FALSE while if the SSP has a solution the algorithm returns TRUE with probability 1/2^log(n). This can be seen as two types of coins. One coin, when tossed always returns TAILS while the other also returns HEADS but with probability 1/2^log(n). Using the Law of Large Numbers one can identify the coin type and as such assert the existence of a solution to the SSP. The algorithm is developed in the more general framework of maximizing the distance to a given point over an intersection of balls.

11/07/2020

### Fast Low-Space Algorithms for Subset Sum

We consider the canonical Subset Sum problem: given a list of positive i...
11/05/2018

### On a generalization of iterated and randomized rounding

We give a general method for rounding linear programs that combines the ...
12/21/2021

### Efficient reductions and algorithms for variants of Subset Sum

Given (a_1, …, a_n, t) ∈ℤ_≥ 0^n + 1, the Subset Sum problem (𝖲𝖲𝖴𝖬) is to...
02/21/2019

### Forecasting the Volatilities of Philippine Stock Exchange Composite Index Using the Generalized Autoregressive Conditional Heteroskedasticity Modeling

This study was conducted to find an appropriate statistical model to for...
02/11/2022

### The Factorial-Basis Method for Finding Definite-Sum Solutions of Linear Recurrences With Polynomial Coefficients

The problem of finding a nonzero solution of a linear recurrence Ly = 0 ...
07/24/2023

### On Maximizing the Distance to a Given Point over an Intersection of Balls II

In this paper the problem of maximizing the distance to a given fixed po...
03/11/1999

### A complete anytime algorithm for balanced number partitioning

Given a set of numbers, the balanced partioning problem is to divide the...