A DP Approach to Hamiltonian Path Problem
Dmitriy Nuriyev
TL;DR
This paper presents a polynomial-time dynamic programming algorithm for solving the Hamiltonian Path problem in directed graphs, utilizing innovative colored hypergraph structures for state management.
Contribution
It introduces a novel DP approach with original hypergraph structures, providing both theoretical complexity proofs and a practical C++ implementation.
Findings
Polynomial worst-case time and space complexity
Successful implementation in C++ demonstrating practicality
Innovative use of colored hypergraphs for DP state management
Abstract
A Dynamic Programming based polynomial worst case time and space algorithm is described for computing Hamiltonian Path of a directed graph. Complexity constructive proofs along with a tested C++ implementation are provided as well. The result is obtained via the use of original colored hypergraph structures in order to maintain and update the necessary DP states.
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Formal Methods in Verification · Optimization and Search Problems