{ "_id": "6ad26c5a475807f7554a6235", "Package": "cayleyR", "Type": "Package", "Title": "Cayley Graph Analysis for Permutation Puzzles", "Version": "0.3.0", "Authors@R": "c(\nperson(\n\"Yuri\", \"Baramykov\",\nemail = \"lbsbmsu@mail.ru\",\nrole = c(\"aut\", \"cre\"),\ncomment = c(ORCID = \"0009-0000-7627-4217\")\n),\nperson(\"Lucas\", \"Garron\", role = c(\"ctb\", \"cph\"),\ncomment = \"twips search machinery in src/kociemba_core.h, src/kociemba4.h\"),\nperson(\"cubing.js authors\", role = \"cph\",\ncomment = \"twips, https://github.com/cubing/twips\")\n)", "Description": "Analyzes Cayley graphs of permutation puzzles. Any puzzle\nwhose moves permute a fixed set of positions can be declared as\na permutation group, and the same tools then work on it: cycle\ndetection, state space exploration and path search. Two puzzles\nare built in: TopSpin and Rubik's cubes of any size. The 3x3x3\nis solved by four human methods and by a two-phase search after\nHerbert Kociemba; the 4x4x4 is solved by reduction. The\nIterative Cycle Intersection (ICI) method is described in Yuri\nBaramykov (2026) .", "License": "MIT + file LICENSE", "Encoding": "UTF-8", "Roxygen": "list(markdown = TRUE)", "RoxygenNote": "7.3.3", "Config/testthat/edition": "3", "VignetteBuilder": "knitr", "URL": "https://github.com/Zabis13/cayleyR,\nhttps://arxiv.org/abs/2607.13219", "BugReports": "https://github.com/Zabis13/cayleyR/issues", "Repository": "https://zabis13.r-universe.dev", "Date/Publication": "2026-10-16 13:31:14 UTC", "RemoteUrl": "https://github.com/zabis13/cayleyr", "RemoteRef": "HEAD", "RemoteSha": "8da1c75d2da91badd8af7f3aa55912386713f6ae", "NeedsCompilation": "yes", "Packaged": { "Date": "2026-10-16 17:47:46 UTC", "User": "root" }, "Author": "Yuri Baramykov [aut, cre] (ORCID:\n),\nLucas Garron [ctb, cph] (twips search machinery in src/kociemba_core.h,\nsrc/kociemba4.h),\ncubing.js authors [cph] (twips, https://github.com/cubing/twips)", "Maintainer": "Yuri Baramykov ", "_user": "zabis13", "_type": "src", 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"shift_left_simple", "shift_right", "shift_right_simple", "short_path_bfs", "short_position", "sparse_bfs", "state_store_indices_for_cycle", "state_store_perm_length", "state_store_size", "state_store_unique_count", "store_add_from_df", "store_analyze_combos", "store_analyze_combos_gpu", "store_clear", "store_clear_opd", "store_collect_ops", "store_combos_for_state", "store_filter_middle", "store_find_best_match", "store_find_intersections", "store_get_meta", "store_get_state", "store_group", "store_lookup", "store_reconstruct_path", "store_set_opd", "store_to_dataframe", "topspin_group", "validate_and_simplify_path" ], "_help": [ { "page": "analyze_top_combinations", "title": "Analyze Top Operation Combinations", "topics": [ "analyze_top_combinations" ] }, { "page": "apply_operations", "title": "Apply Sequence of Operations", "topics": [ "apply_operations" ] }, { "page": "apply_operations_batch_gpu", "title": "Apply operations to batch of states on GPU", "topics": [ "apply_operations_batch_gpu" ] }, { "page": "bidirectional_bfs", "title": "Bidirectional BFS Shortest Path", "topics": [ "bidirectional_bfs" ] }, { "page": "breakpoint_distance", "title": "Breakpoint Distance Between Two States", "topics": [ "breakpoint_distance" ] }, { "page": "build_permutation_matrix", "title": "Build permutation matrix for a single operation", "topics": [ "build_permutation_matrix" ] }, { "page": "calculate_angular_distance_z", "title": "Angular Distance Between Two Celestial Points", "topics": [ "calculate_angular_distance_z" ] }, { "page": "calculate_differences", "title": "Calculate Manhattan Distances for All States", "topics": [ "calculate_differences" ] }, { "page": "calculate_midpoint_z", "title": "Midpoint Between Two Celestial Coordinates", "topics": [ "calculate_midpoint_z" ] }, { "page": "cayley_bfs_full", "title": "Full Breadth-First Search Over the Cayley Graph", "topics": [ "cayley_bfs_full" ] }, { "page": "cayley_gpu_available", "title": "Check if GPU acceleration is available", "topics": [ "cayley_gpu_available" ] }, { "page": "cayley_gpu_free", "title": "Free GPU backend resources", "topics": [ "cayley_gpu_free" ] }, { "page": "cayley_gpu_init", "title": "Initialize GPU backend", "topics": [ "cayley_gpu_init" ] }, { "page": "cayley_gpu_status", "title": "Get GPU status information", "topics": [ "cayley_gpu_status" ] }, { "page": "cayley_graph_diameter", "title": "Cayley Graph Diameter and Maximally Distant State Pairs", "topics": [ "cayley_graph_diameter" ] }, { "page": "check_duplicates", "title": "Find Duplicate States Between Two Tables", "topics": [ "check_duplicates" ] }, { "page": "compose_permutation_matrix", "title": "Compose permutation matrices for a sequence of operations", "topics": [ "compose_permutation_matrix" ] }, { "page": "convert_digits", "title": "Convert String to Integer Vector of Digits", "topics": [ "convert_digits" ] }, { "page": "convert_LRX_to_celestial", "title": "Convert LRX Counts to Celestial Coordinates", "topics": [ "convert_LRX_to_celestial" ] }, { "page": "convex_hull_3d", "title": "Convex Hull of a 3-D Point Cloud", "topics": [ "convex_hull_3d" ] }, { "page": "create_state_store", "title": "Create a New State Store", "topics": [ "create_state_store" ] }, { "page": "cube_adi", "title": "Autodidactic Iteration on a Permutation Puzzle", "topics": [ "cube_adi" ] }, { "page": "cube_adi_astar", "title": "Batch Weighted A* With a Learned Heuristic", "topics": [ "cube_adi_astar" ] }, { "page": "cube_adi_load", "title": "Load a Trained ADI Network", "topics": [ "cube_adi_load" ] }, { "page": "cube_adi_model", "title": "Build the Value and Policy Networks", "topics": [ "cube_adi_model" ] }, { "page": "cube_adi_save", "title": "Save a Trained ADI Network", "topics": [ "cube_adi_save" ] }, { "page": "cube_adi_solve", "title": "Solve a Cube With a Trained Network", "topics": [ "cube_adi_solve" ] }, { "page": "cube_adi_train", "title": "Train Value and Policy by Autodidactic Iteration", "topics": [ "cube_adi_train" ] }, { "page": "cube_alg_table", "title": "The Algorithm Tables", "topics": [ "cube_alg_table" ] }, { "page": "cube_apply_word", "title": "Apply a Word of Moves to a Cube State", "topics": [ "cube_apply_word" ] }, { "page": "cube_build_lslice", "title": "Build the Layer Beside a Face, at Any Size", "topics": [ "cube_build_lslice" ] }, { "page": "cube_central_moves", "title": "Slice Turns That Reorient the Whole Cube", "topics": [ "cube_central_moves" ] }, { "page": "cube_centre_counts", "title": "Count the Centre Pieces That Are Home", "topics": [ "cube_centre_counts" ] }, { "page": "cube_centre_cycles", "title": "Three-Cycles of Centres, One Per Orbit", "topics": [ "cube_centre_cycles" ] }, { "page": "cube_centre_map_family", "title": "The Centres of a Cube of Any Size, Derived", "topics": [ "cube_centre_map_family" ] }, { "page": "cube_centre_positions", "title": "Sticker Positions of the Six Centres", "topics": [ "cube_centre_positions" ] }, { "page": "cube_centre_shots", "title": "Commutators That Carry Centres Off One Face and Spare Another", "topics": [ "cube_centre_shots" ] }, { "page": "cube_centre_structure", "title": "Centre Stickers of an N x N x N Cube", "topics": [ "cube_centre_structure" ] }, { "page": "cube_colours", "title": "Colours and Positions: the Two Ways to Write a Cube Down", "topics": [ "cube_colours", "cube_colour_state" ] }, { "page": "cube_edge_algs", "title": "The Published Edge-Pairing Algorithms, at Any Size", "topics": [ "cube_edge_algs" ] }, { "page": "cube_edge_counts", "title": "How Many Edges Are Whole", "topics": [ "cube_edge_counts" ] }, { "page": "cube_edge_map", "title": "Where a Turn Sends Each Edge Piece", "topics": [ "cube_edge_map" ] }, { "page": "cube_edge_map_family", "title": "The Edges of a Cube of Any Size, Derived", "topics": [ "cube_edge_map_family" ] }, { "page": "cube_edge_structure", "title": "Edge Pieces of an N x N x N Cube", "topics": [ "cube_edge_structure" ] }, { "page": "cube_empty_u_slice", "title": "Empty the Top Face onto the Sides", "topics": [ "cube_empty_u_slice" ] }, { "page": "cube_expand_alg", "title": "Expand an Algorithm into the Package's Alphabet", "topics": [ "cube_expand_alg" ] }, { "page": "cube_expand_move", "title": "Wide Turns and Whole-Cube Rotations", "topics": [ "cube_expand_move", "cube_expand_word", "cube_wide_move", "cube_wide_word" ] }, { "page": "cube_group", "title": "The Group of an N x N x N Cube", "topics": [ "cube_group" ] }, { "page": "cube_identity", "title": "Solved State of an N x N x N Cube", "topics": [ "cube_identity" ] }, { "page": "cube_is_colour_solved", "title": "Test Whether Every Face of a Cube is a Single Colour", "topics": [ "cube_is_colour_solved" ] }, { "page": "cube_is_reduced", "title": "Is a Cube Reduced?", "topics": [ "cube_is_reduced" ] }, { "page": "cube_kociemba", "title": "Solve a 3x3x3 by Two-Phase Search", "topics": [ "cube_kociemba" ] }, { "page": "cube_kociemba_init", "title": "Build the Kociemba Prune Tables", "topics": [ "cube_kociemba_init" ] }, { "page": "cube_kociemba_report", "title": "What the Last Kociemba Solve Did", "topics": [ "cube_kociemba_report" ] }, { "page": "cube_kociemba4", "title": "Solve a 4x4x4 by Four-Phase Search", "topics": [ "cube_kociemba4" ] }, { "page": "cube_kociemba4_reduce", "title": "Reduce a 4x4x4 by Four-Phase Search", "topics": [ "cube_kociemba4_reduce" ] }, { "page": "cube_kociemba4_report", "title": "What the Last 4x4x4 Reduction Did", "topics": [ "cube_kociemba4_report" ] }, { "page": "cube_layer_move", "title": "A Single Layer Turn, by Axis and Layer", "topics": [ "cube_layer_move" ] }, { "page": "cube_lslice_cells", "title": "The Layer Beside a Face, and What Leaves It Alone", "topics": [ "cube_free_moves", "cube_lslice_cells" ] }, { "page": "cube_move_names", "title": "Move Names of an N x N x N Cube", "topics": [ "cube_move_names" ] }, { "page": "cube_moves", "title": "Move Table of an N x N x N Cube", "topics": [ "cube_moves" ] }, { "page": "cube_nnn", "title": "Cubes of Any Size", "topics": [ "cube_nnn" ] }, { "page": "cube_orbits", "title": "Orbits of an N x N x N Cube", "topics": [ "cube_orbits" ] }, { "page": "cube_orbits_family", "title": "Piece Orbits of a Cube of Any Size", "topics": [ "cube_orbits_family" ] }, { "page": "cube_pair_edges", "title": "Pair the Edges of a Cube of Any Size", "topics": [ "cube_pair_edges" ] }, { "page": "cube_piece_layout", "title": "The Piece Layout a Cube State Is Read Through", "topics": [ "cube_piece_layout" ] }, { "page": "cube_pieces", "title": "Pieces of an N x N x N Cube", "topics": [ "cube_pieces" ] }, { "page": "cube_pieces_home", "title": "Pieces Home on a Cube", "topics": [ "cube_pieces_home" ] }, { "page": "cube_predicates", "title": "Stage Predicates of a Cube State", "topics": [ "cube_predicates" ] }, { "page": "cube_progress", "title": "How Much of Each Orbit Is Solved", "topics": [ "cube_progress" ] }, { "page": "cube_read_state", "title": "Read a Cube State as Pieces", "topics": [ "cube_read_state" ] }, { "page": "cube_reduce_best", "title": "Reduce a 4x4x4, Trying Every Starting Face", "topics": [ "cube_reduce_best" ] }, { "page": "cube_reduce_cpp", "title": "Reduce a 4x4x4 by the human method", "topics": [ "cube_reduce_cpp" ] }, { "page": "cube_santa", "title": "The Santa 2023 Cube Notation", "topics": [ "cube_santa" ] }, { "page": "cube_santa_group", "title": "A Cube Group in Santa 2023 Notation", "topics": [ "cube_santa_group" ] }, { "page": "cube_santa_move_names", "title": "Santa 2023 Move Names for a Cube", "topics": [ "cube_santa_move_names" ] }, { "page": "cube_santa_moves", "title": "Translate Between Santa 2023 and Package Move Names", "topics": [ "cube_moves_santa", "cube_santa_moves" ] }, { "page": "cube_santa_path", "title": "Translate a Santa 2023 Solution Path", "topics": [ "cube_santa_path", "cube_santa_path_out" ] }, { "page": "cube_santa_perm", "title": "Sticker Relabelling Between Santa 2023 and This Package", "topics": [ "cube_santa_perm" ] }, { "page": "cube_santa_state", "title": "Read and Write Santa 2023 Cube States", "topics": [ "cube_santa_state", "cube_santa_state_out" ] }, { "page": "cube_slice_cells_cpp", "title": "The Layer Beside a Face, as the 4x4x4 Solver Sees It", "topics": [ "cube_slice_cells_cpp" ] }, { "page": "cube_slice_map", "title": "Where a Slice Turn Sends Each Centre", "topics": [ "cube_slice_map" ] }, { "page": "cube_solve_centres", "title": "Solve the Centres of a 4x4x4 Cube", "topics": [ "cube_solve_centres" ] }, { "page": "cube_solve_cfop", "title": "Solve a 3x3x3 Cube by CFOP", "topics": [ "cube_solve_cfop" ] }, { "page": "cube_solve_lbl", "title": "Solve a 3x3x3 Cube Layer by Layer", "topics": [ "cube_solve_lbl" ] }, { "page": "cube_solve_m2", "title": "Solve a 3x3x3 Cube by M2", "topics": [ "cube_solve_m2" ] }, { "page": "cube_solve_old_pochmann", "title": "Solve a 3x3x3 Cube by Old Pochmann", "topics": [ "cube_solve_old_pochmann" ] }, { "page": "cube_solve4", "title": "Solve a 4x4x4 Cube by Reduction", "topics": [ "cube_solve4" ] }, { "page": "cube_solve4_cascade", "title": "Solve a 4x4x4 by reduction, falling back when the search does not pay off", "topics": [ "cube_solve4_cascade" ] }, { "page": "cube_wide_turn", "title": "Wide Turns of an N x N x N Cube", "topics": [ "cube_wide_turn" ] }, { "page": "cube_word_order", "title": "Order of a Word of Moves", "topics": [ "cube_word_order" ] }, { "page": "cycle_shortcut", "title": "Shorten a Path by Cutting Across Cycles", "topics": [ "cycle_shortcut" ] }, { "page": "distance_methods", "title": "Distance Methods for Bridge Selection", "topics": [ "cayley_distance", "cayley_distance_methods", "distance_methods" ] }, { "page": "enclosing_hull_3d", "title": "Enclosing Hull Through Every Point", "topics": [ "enclosing_hull_3d" ] }, { "page": "find_best_match_cube4_model", "title": "Score Candidate States With a Trained 4x4x4 Model", "topics": [ "find_best_match_cube4_model" ] }, { "page": "find_best_match_human", "title": "Score Candidate States the Way a Person Solves", "topics": [ "find_best_match_human" ] }, { "page": "find_best_random_combinations", "title": "Find Best Random Operation Sequences", "topics": [ "find_best_random_combinations" ] }, { "page": "find_closest_to_coords", "title": "Find Closest State to Target Coordinates", "topics": [ "find_closest_to_coords" ] }, { "page": "find_combination_in_states", "title": "Find a State in Reachable States Table", "topics": [ "find_combination_in_states" ] }, { "page": "find_path_bfs", "title": "Find Path via BFS Highways", "topics": [ "find_path_bfs" ] }, { "page": "find_path_iterative", "title": "Iterative Path Finder Between Permutation States", "topics": [ "find_path_iterative" ] }, { "page": "generate_state", "title": "Generate Reachable Random State", "topics": [ "generate_state" ] }, { "page": "generate_unique_states_df", "title": "Generate Data Frame of Unique Random States", "topics": [ "generate_unique_states_df" ] }, { "page": "generate_walk", "title": "Random Walks From the Solved State, With the Moves They Took", "topics": [ "generate_walk" ] }, { "page": "get_reachable_states", "title": "Find Cycle in Permutation Group", "topics": [ "get_reachable_states" ] }, { "page": "get_reachable_states_light", "title": "Find Cycle Length (Lightweight Version)", "topics": [ "get_reachable_states_light" ] }, { "page": "group_apply", "title": "Apply a Move Sequence Through a Group", "topics": [ "group_apply" ] }, { "page": "group_compose", "title": "Compose a Move Sequence into One Permutation", "topics": [ "group_compose" ] }, { "page": "group_identity", "title": "Solved State of a Group", "topics": [ "group_identity" ] }, { "page": "group_inverse_seq", "title": "Invert a Move Sequence", "topics": [ "group_inverse_seq" ] }, { "page": "group_move_index", "title": "Resolve Move Names to Indices Within a Group", "topics": [ "group_move_index" ] }, { "page": "group_moves", "title": "Move Alphabet of a Group", "topics": [ "group_moves" ] }, { "page": "group_order", "title": "Order of a Move Sequence in a Group", "topics": [ "group_order" ] }, { "page": "group_parse_word", "title": "Parse a Word Written as One String", "topics": [ "group_parse_word" ] }, { "page": "human_algorithm", "title": "Solve a State with the Human TopSpin Algorithm", "topics": [ "human_algorithm" ] }, { "page": "human_algorithm_to", "title": "Human Algorithm Path Between Two Arbitrary States", "topics": [ "human_algorithm_to" ] }, { "page": "human_phase1_navigate", "title": "Follow the Phase 1 Navigator to the Tail", "topics": [ "human_phase1_navigate" ] }, { "page": "human_phase1_rank", "title": "Rank Candidate Moves by the Phase 1 Criterion", "topics": [ "human_phase1_rank" ] }, { "page": "invert_path", "title": "Invert a Path of Operations", "topics": [ "invert_path" ] }, { "page": "is_perm_group", "title": "Test Whether an Object is a Permutation Group", "topics": [ "is_perm_group" ] }, { "page": "kociemba4_phases", "title": "The 4x4x4 reduction phases, one call at a time", "topics": [ "cube_at_phase_goal_cpp", "cube_kociemba4_fill_phase3_cpp", "cube_kociemba4_phase12_cpp", "cube_kociemba4_phase3_cpp", "cube_kociemba4_tables_cpp", "cube_phase3_coord_cpp", "cube_to_pieces4_cpp", "cube_wing_geometry_cpp", "kociemba4_phases" ] }, { "page": "landmark_states", "title": "Generate Landmark States for a Permutation of Size n", "topics": [ "landmark_states" ] }, { "page": "manhattan_distance", "title": "Manhattan Distance Between Two States", "topics": [ "manhattan_distance" ] }, { "page": "manhattan_distance_matrix_gpu", "title": "Compute Pairwise Manhattan Distance Matrix on GPU", "topics": [ "manhattan_distance_matrix_gpu" ] }, { "page": "openmp_threads", "title": "Number of OpenMP Threads Available", "topics": [ "openmp_threads" ] }, { "page": "perm_group", "title": "Create a Permutation Group from a Table of Moves", "topics": [ "perm_group" ] }, { "page": "perm_group_intro", "title": "Permutation Groups", "topics": [ "perm_group_intro" ] }, { "page": "print.perm_group", "title": "Print a Permutation Group", "topics": [ "print.perm_group" ] }, { "page": "reconstruct_bfs_path", "title": "Reconstruct path from sparse BFS result", "topics": [ "reconstruct_bfs_path" ] }, { "page": "reverse_prefix", "title": "Reverse First k Elements (with Coordinates)", "topics": [ "reverse_prefix" ] }, { "page": "reverse_prefix_simple", "title": "Reverse First k Elements (Simple)", "topics": [ "reverse_prefix_simple" ] }, { "page": "run_length", "title": "Length of the Sorted Run on the Ring", "topics": [ "run_length" ] }, { "page": "save_bridge_states", "title": "Save Bridge States to CSV", "topics": [ "save_bridge_states" ] }, { "page": "select_unique", "title": "Select Unique States by V-columns", "topics": [ "select_unique" ] }, { "page": "shift_left", "title": "Shift State Left (with Coordinates)", "topics": [ "shift_left" ] }, { "page": 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