Parallel implementation of the modified subset sum problem in CUDA

Abstract

In the recent years, computing is shifting from "central processing" on the CPU to "co-processing" on the CPU and GPU. This computing paradigm shift is due to the development of CUDA (Compute Unified Device Architecture) parallel computing architecture. CUDA is a programming model for parallel computing in Graphics Processing Units (GPUs). In this work, we have implemented parallel solution of the NP-complete modified subset sum algorithm using CUDA. With our implementation, for a certain problem size, we have obtained speedup of 20 times, compared to the CPU version.

Optimality and Complexity Analysis of a Branch-and-Bound Method in Solving Some Instances of the Subset Sum Problem

“…Thus, by the same way as in the case of odd n we can prove that for (18) we can conclude that the minimum value of L P[n;k] (l) is achieved at l = n ′ .…”

“…Taking into account inequalities (18), from δ(n ′ + 1) > 0 and δ(n ′ ) < 0 we conclude that the minimum value of L P[n;k] (l) for k+2 ≤ l ≤ n−2(k+1) is achieved at l = n ′ +1. b) Now let n be even, i.e.…”

“…Empirical parallelizations of two-list method of solving of SSP for GPU and hybrid CPU/GPU computational models are proposed in [15][16][17]. A parallel GPU algorithm of solving some modification of SSP is proposed in [18]. More information on the state of the art in this field can be found in [19] where an efficient modification of the balanced algorithm [1] for SSP is proposed.…”