Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Computing high dimensional volumes is a hard problem, even for approximation. Several randomized approximation techniques for #P-hard problems have been developed in the three decades, while some deterministic approximation algorithms are recently developed only for a few #P-hard problems. Motivated by a new technique for a deterministic approximation, this paper is concerned with the volume computation of 0-1 knapsack polytopes, which is known to be #P-hard.  presents a new technique based on approximate convolutions for a deterministic approximation of volume computations, and provides a fully polynomial-time approximation scheme for the volume computation of 0-1 knapsack polytopes.  also give an extension of the result to multi-constrained knapsack polytopes with a constant number of constraints.
['Ei Ando', 'Shuji Kijima']
I am writing a research paper on a idea An FPTAS for the Volume Computation of 0-1 Knapsack Polytopes Based on Approximate Convolution
[{"from": "human", "value": "I am writing a research paper on a idea An FPTAS for the Volume Computation of 0-1 Knapsack Polytopes Based on Approximate Convolution"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Computing high dimensional volumes is a hard problem, even for approximation. Several randomized approximation techniques for #P-hard problems have been developed in the three decades, while some deterministic approximation algorithms are recently developed only for a few #P-hard problems. Motivated by a new technique for a deterministic approximation, this paper is concerned with the volume computation of 0-1 knapsack polytopes, which is known to be #P-hard.  presents a new technique based on approximate convolutions for a deterministic approximation of volume computations, and provides a fully polynomial-time approximation scheme for the volume computation of 0-1 knapsack polytopes.  also give an extension of the result to multi-constrained knapsack polytopes with a constant number of constraints."}]