Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present space efficient Monte Carlo algorithms that solve Subset Sum and Knapsack instances with $n$ items using $O^*(2^{0.86n})$ time and polynomial space, where the $O^*(\cdot)$ notation suppresses factors polynomial in the input size. Both algorithms assume random read-only access to random bits. Modulo this mild assumption, this resolves a long-standing open problem in exact algorithms for NP-hard problems. These results can be extended to solve Binary Linear Programming on $n$ variables with few constraints in a similar running time.  also show that for any constant $k\geq 2$, random instances of $k$-Sum can be solved using $O(n^{k-0.5}polylog(n))$ time and $O(\log n)$ space, without the assumption of random access to random bits. #R##N#Underlying these results is an algorithm that determines whether two given lists of length $n$ with integers bounded by a polynomial in $n$ share a common value. Assuming random read-only access to random bits,  show that this problem can be solved using $O(\log n)$ space significantly faster than the trivial $O(n^2)$ time algorithm if no value occurs too often in the same list.
['Nikhil Bansal', 'Shashwat Garg', 'Jesper Nederlof', 'Nikhil Vyas']
I am writing a research paper on a idea Faster Space-Efficient Algorithms for Subset Sum, k-Sum and Related Problems
[{"from": "human", "value": "I am writing a research paper on a idea Faster Space-Efficient Algorithms for Subset Sum, k-Sum and Related Problems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present space efficient Monte Carlo algorithms that solve Subset Sum and Knapsack instances with $n$ items using $O^*(2^{0.86n})$ time and polynomial space, where the $O^*(\\cdot)$ notation suppresses factors polynomial in the input size. Both algorithms assume random read-only access to random bits. Modulo this mild assumption, this resolves a long-standing open problem in exact algorithms for NP-hard problems. These results can be extended to solve Binary Linear Programming on $n$ variables with few constraints in a similar running time.  also show that for any constant $k\\geq 2$, random instances of $k$-Sum can be solved using $O(n^{k-0.5}polylog(n))$ time and $O(\\log n)$ space, without the assumption of random access to random bits. #R##N#Underlying these results is an algorithm that determines whether two given lists of length $n$ with integers bounded by a polynomial in $n$ share a common value. Assuming random read-only access to random bits,  show that this problem can be solved using $O(\\log n)$ space significantly faster than the trivial $O(n^2)$ time algorithm if no value occurs too often in the same list."}]