Objective　In　large-scale　motion　simulation　problems,　the　search　efficiency　for　nearest　neighbor　points　critically　influences　the　overall　operational　efficiency.　This　study　applies　correlation　analysis　to　establish　an　adaptive　relationship　between　the　maximum　depth　of　the　kd-tree　(dmax)　and　the　total　number　of　particles　(N).　A　novel　automatic　termination　criterion　for　the　kd-tree,　known　as　ATC-kd-tree,　addresses　the　impact　of　the　leaf　node　size　threshold　(n0)　on　nearest　neighbor　search　efficiency.　This　method　effectively　addresses　the　challenges　of　recalibrating　dmax　as　N　varies,　enhancing　the　efficiency　and　applicability　of　the　kd-tree　in　various　scenarios.　Methods　The　ATC-kd-tree　framework　is　designed　to　dynamically　adjust　the　kd-tree　structure　based　on　the　current　particle　count,　ensuring　optimal　performance　for　efficient　searches　in　real-time　applications.　This　method　involves　a　comprehensive　analysis　of　particle　distributions,　enabling　the　algorithm　to　adaptively　modify　dmax　based　on　the　specific　characteristics　of　the　particle　set　at　any　given　time.　The　ATC-kd-tree　effectively　responds　to　the　spatial　arrangement　of　particles,　enhancing　search　accuracy　and　speed　by　integrating　data-driven　adjustments.　In　addition,　a　two-step　parameter　optimization　algorithm　that　combines　grid　search　with　coordinate　descent　methods　(GSCD)　is　introduced.　This　hybrid　approach　expedites　the　calibration　of　variable　parameters　crucial　for　optimizing　ATC-kd-tree　performance,　facilitating　a　more　precise　search　process.　The　GSCD　method　accelerates　the　pace　of　parameter　adjustment　and　increases　accuracy　by　ensuring　that　the　most　appropriate　parameters　are　selected　based　on　empirical　evidence.　A　comprehensive　series　of　experimental　trials　is　conducted　involving　various　particle　distribution　models,　such　as　uniform,　random,　and　clustered　configurations.　These　trials　are　designed　to　assess　the　efficiency　of　the　ATC-kd-tree　and　the　GSCD　optimization　process.　Key　performance　metrics,　including　search　time,　cache　miss　rates,　and　overall　computational　efficiency,　are　diligently　monitored　and　analyzed.　Rigorous　comparisons　against　baseline　methods,　comprising　traditional　kd-trees　and　alternative　sorting　algorithms,　are　executed　to　ensure　a　thorough　evaluation　of　the　proposed　techniques.　Results　and　Discussions　The　study’s　findings　demonstrated　that　the　ATC-kd-tree　framework　significantly　improves　the　efficiency　of　nearest　neighbor　searches,　especially　in　large-scale　motion　simulations　characterized　by　dynamically　fluctuating　particle　distributions.　Experiments　involving　particle　distribution　shapes,　such　as　rectangular,　cuboidal,　notched　cuboidal,　spherical,　and　annular,　are　frequently　employed　in　fluid　dynamics　studies　to　corroborate　their　efficiency.　The　ATC-kd-tree　achieved　an　impressive　average　reduction　in　search　time　of　up　to　30.3%　compared　to　traditional　unsorted　kd-tree　implementations　across　all　tested　configurations.　When　analyzing　datasets　comprising　40　000　and　575　000　particles,　the　search　times　exhibit　significant　enhancement:　the　ATC-kd-tree　reduces　the　search　time　from　1.75　seconds　with　traditional　methods　to　1.22　seconds　for　the　former　dataset　and　from　7.12　seconds　to　4.97　seconds　for　the　latter.　This　performance　improvement　is　particularly　marked　in　environments　with　high　spatial　divergence　among　particles,　where　traditional　methods　often　falter　with　inconsistent　search　paths.　In　addition,　an　average　reduction　of　24.2%　in　cache　miss　rates　is　observed　when　employing　the　ATC-kd-tree.　In　scenarios　with　larger　particle　counts,　the　cache　miss　rate　decreases　from　35%　in　the　traditional　unsorted　kd-tree　to　26%　with　the　ATC-kd-tree,　which　directly　contributes　to　enhanced　computational　efficiency,　facilitating　quicker　data　retrieval　during　neighbor　searches.　The　ATC-kd-tree　demonstrated　exceptional　adaptability　to　rapidly　evolving　particle　configurations　in　computational　fluid　dynamics　(CFD)　simulations.　In　a　specific　experiment　involving　50　000　particles　exposed　to　external　forces　causing　irregular　movements,　the　ATC-kd-tree　shows　a　20%　reduction　in　cache　misses　and　a　15%　decrease　in　overall　computational　time　compared　to　traditional　methods.　This　capacity　to　effectively　manage　irregular　particle　movements　underscores　the　ATC-kd-tree’s　robustness　for　real-time　applications　that　demand　rapid　adaptability　to　dynamic　changes.　The　GSCD　optimization　method　further　augments　the　performance　of　the　ATC-kd-tree,　as　the　analysis　indicates　that　GSCD　accelerates　parameter　calibration　by　205%　relative　to　traditional　grid　search　methods.　In　experiments,　the　GSCD　method　reduces　calibration　time　significantly,　from　over　120　seconds　in　traditional　methods　to　approximately　40　seconds.　This　enhancement　enables　rapid　adjustments　to　the　parameters　of　the　kd-tree　and　ensures　that　the　tree　remains　optimally　configured　to　the　specific　characteristics　of　the　particle　distributions　encountered　during　simulations.　The　adaptability　of　the　ATC-kd-tree　is　evident　across　various　particle　distribution　scenarios.　This　algorithm　consistently　surpasses　traditional　unsorted　kd-trees　and　alternative　sorting　methods　in　clustered　configurations,　such　as　the　Z-index　sort.　In　these　configurations,　the　search　time　is　significantly　reduced,　demonstrating　the　ATC-kd-tree’　s　ability　to　dynamically　reorganize　its　structure　based　on　real-time　analysis　of　particle　distributions.　This　capability　maximizes　cache　utilization　and　minimizes　cache　misses.　The　findings　indicated　that　the　ATC-kd-tree　is　particularly　effective　in　scenarios　involving　non-uniform　particle　distributions,　as　its　capacity　to　adjust　dmax　based　on　the　number　of　particles　eliminates　the　cumbersome　recalibration　processes　typically　required　by　traditional　methods.　Hence,　this　leads　to　a　smoother　and　more　efficient　search　process,　even　as　particle　distributions　experience　significant　changes.　These　results　highlight　the　critical　importance　of　incorporating　adaptive　techniques　into　kd-tree　implementations　to　improve　search　efficiency　in　large-scale　simulations.　The　improvements　in　search　time　and　cache　utilization　achieved　by　the　ATC-kd-tree　provide　compelling　evidence　of　its　potential　to　transform　how　nearest　neighbor　searches　are　conducted　in　dynamic　environments.　Conclusions　The　introduction　of　the　ATC-kd-tree　provides　a　valuable　approach　to　optimizing　kd-tree-based　nearest　neighbor　searches,　particularly　in　dynamic　and　large-scale　motion　simulations.　This　research　aims　to　enhance　search　efficiency　and　deliver　a　scalable　solution　for　managing　varying　particle　distributions　by　integrating　an　automatic　termination　criterion　with　a　rapid　parameter　optimization　method.　The　results　showed　that　the　ATC-kd-tree　can　improve　operational　performance,　reducing　computational　overhead　and　cache　misses,　which　is　crucial　for　real-time　applications　where　efficiency　is　paramount.　In　addition,　the　principles　explored　in　this　study　can　extend　beyond　the　kd-tree　framework,　demonstrating　new　avenues　for　research　into　adaptive　data　access　techniques　that　can　prove　beneficial　across　various　computational　domains,　including　machine　learning,　computer　graphics,　and　robotics.　Future　efforts　will　concentrate　on　integrating　the　ATC-kd-tree　with　advanced　cache　management　strategies　to　optimize　performance　and　investigate　methods　to　reduce　computational　complexity　in　high-dimensional　contexts,　which　remains　a　critical　area　of　investigation.　This　study　aims　to　address　these　challenges　and　broaden　the　applicability　of　kd-tree　methods　in　real-time　environments,　making　them　more　adaptable　to　complex　and　dynamic　conditions.　It　contributes　to　enhancing　the　functionality　of　kd-trees　and　provides　insights　into　the　broader　field　of　data　structure　optimization,　laying　a　foundation　for　future　developments　in　efficient　data　processing　techniques.　©　2024　Sichuan　University.　All　rights　reserved.