BACKTRACKING AS A GENERAL SEARCH METHOD: EIGHT QUEENS, SUM OF SUBSETS, GRAPH COLORING AND HAMILTONIAN CYCLE PROBLEMS

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Published ID: IJNRD2608217

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Temilade Fasina, Akinwole, Agnes Kikelomo, Idowu Mayowa Opakunle, Sakpere pwilson

treatment of backtracking as a general method and as a solver for four classical problems.

Backtracking is a foundational exact search method for constraint satisfaction, enumeration and discrete optimization. Its practical importance comes from a simple but powerful idea: construct a partial candidate, test whether it remains promising, and withdraw the most recent decision when no valid extension remains. This article presents an academic treatment of the general backtracking method and four classical applications: the eight queens problem, the sum of subsets problem, graph coloring and the Hamiltonian cycle problem. The study combines formal mathematical modelling, algorithmic pseudocode, complexity analysis and reproducible computational experiments. The experimental dataset consists of deterministic benchmark instances generated for N queens boards from n equals 4 to n equals 12, subset sum instances from n equals 8 to n equals 22, random graph coloring instances with 20 vertices and varying edge probability, and Hamiltonian cycle instances from n equals 8 to n equals 15 near threshold densities. Results confirm that backtracking can be efficient when pruning removes large subtrees, but it remains vulnerable to exponential state space growth. The eight queens solver generated 92 solutions for n equals 8 and 14,200 solutions for n equals 12. Subset sum states grew from 139 to 345,785 over the tested range. DSATUR style variable ordering sharply reduced graph coloring calls in unsatisfiable cases, while Hamiltonian search showed instance sensitivity near phase transition regions. Keywords: Backtracking, Constraint Satisfaction, Eight Queens, Subset Sum, Graph Coloring, Hamiltonian Cycle, Recursive Search

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Temilade Fasina, Akinwole, Agnes Kikelomo, Idowu Mayowa Opakunle, & Sakpere pwilson (August-2026). BACKTRACKING AS A GENERAL SEARCH METHOD: EIGHT QUEENS, SUM OF SUBSETS, GRAPH COLORING AND HAMILTONIAN CYCLE PROBLEMS. INTERNATIONAL JOURNAL OF NOVEL RESEARCH AND DEVELOPMENT, 11(8), c173-c179. https://ijnrd.org/papers/IJNRD2608217.pdf

Volume 11 Issue 8, August-2026

Pages : c173-c179

Paper Reg. ID: IJNRD_327854

Published Paper Id: IJNRD2608217

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Author Type: Foreign Author

Country: Gloucester, England, United Kingdom

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