HILBERT–KRYLOV TOWER DECOMPOSITION AND A PSEUDO-POLYNOMIAL COMPLEXITY BOUND FOR SUBSET SUM | IJCT Volume 12 – Issue 6 | IJCT-V12I6P57
International Journal of Computer Techniques
ISSN 2394-2231
Author
MICHAEL S. YANG
Abstract
We analyze the algorithmic complexity of the Hilbert–Krylov Tower (HKT) decompo- sition applied to the Subset Sum Problem. By combining a contraction-based pruning principle with a residue-class richness heuristic inspired by Krylov subspace partitioning, we prove that the resulting dynamic programming algorithm runs in time O(N · Weff ), where N is the input size and Weff is an explicitly controlled effective width. This establishes a pseudo-polynomial com- plexity bound under deterministic pruning rules. Experimental results demonstrate large empirical speedups over classical meet-in-the-middle methods on structured instances.
Keywords
^KEYWORDS^
Conclusion
We have provided a complete and rigorous complexity analysis of the HKT-based Subset Sum algorithm. The resulting O(N · Weff ) bound follows directly from explicit pruning rules and demon- strates how structured contraction can dramatically reduce effective state space. This framework opens a path toward analyzing similar decompositions for other NP-hard problems.
References
^REFERENCES_LIST^
How to Cite This Paper
MICHAEL S. YANG (2025). HILBERT–KRYLOV TOWER DECOMPOSITION AND A PSEUDO-POLYNOMIAL COMPLEXITY BOUND FOR SUBSET SUM. International Journal of Computer Techniques, 12(6). ISSN: 2394-2231.
