files / problems / kissing-5d / compute / q4 / n1_dfs_k18.json

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{
  "d": 4,
  "n": 1480,
  "n_d5": 40,
  "n_extras": 1440,
  "n_groups": 240,
  "n_stars": 10,
  "n_extra_edges": 884720,
  "n_intra_group_edges": 0,
  "groups_edgeless": true,
  "maxk": 18,
  "n_unions_visited": 933648919,
  "algorithm": "canonical-dfs",
  "slices": {
    "4": {"k": 4, "n1": 36, "n_unions": 160, "n_promising": 0, "tried": 0, "max_seeds": 1, "best_extras": 0, "best_total": 36, "found": false, "complete": true, "empty_by_part_count": true},
    "5": {"k": 5, "n1": 35, "n_unions": 320, "n_promising": 0, "tried": 0, "max_seeds": 2, "best_extras": 0, "best_total": 35, "found": false, "complete": true, "empty_by_part_count": true},
    "6": {"k": 6, "n1": 34, "n_unions": 320, "n_promising": 0, "tried": 0, "max_seeds": 4, "best_extras": 0, "best_total": 34, "found": false, "complete": true, "empty_by_part_count": true},
    "7": {"k": 7, "n1": 33, "n_unions": 3280, "n_promising": 80, "tried": 80, "max_seeds": 8, "best_extras": 7, "best_total": 40, "found": false, "complete": true, "empty_by_part_count": false},
    "8": {"k": 8, "n1": 32, "n_unions": 20810, "n_promising": 10, "tried": 10, "max_seeds": 16, "best_extras": 8, "best_total": 40, "found": false, "complete": true, "empty_by_part_count": false},
    "9": {"k": 9, "n1": 31, "n_unions": 61920, "n_promising": 0, "tried": 0, "max_seeds": 5, "best_extras": 0, "best_total": 31, "found": false, "complete": true, "empty_by_part_count": true},
    "10": {"k": 10, "n1": 30, "n_unions": 164672, "n_promising": 0, "tried": 0, "max_seeds": 10, "best_extras": 0, "best_total": 30, "found": false, "complete": true, "empty_by_part_count": true},
    "11": {"k": 11, "n1": 29, "n_unions": 577520, "n_promising": 960, "tried": 960, "max_seeds": 17, "best_extras": 11, "best_total": 40, "found": false, "complete": true, "empty_by_part_count": false},
    "12": {"k": 12, "n1": 28, "n_unions": 1942760, "n_promising": 4640, "tried": 4640, "max_seeds": 18, "best_extras": 12, "best_total": 40, "found": false, "complete": true, "empty_by_part_count": false},
    "13": {"k": 13, "n1": 27, "n_unions": 5524320, "n_promising": 31400, "tried": 31400, "max_seeds": 20, "best_extras": 13, "best_total": 40, "found": false, "complete": true, "empty_by_part_count": false},
    "14": {"k": 14, "n1": 26, "n_unions": 14998760, "n_promising": 243160, "tried": 243160, "max_seeds": 25, "best_extras": 14, "best_total": 40, "found": false, "complete": true, "empty_by_part_count": false},
    "15": {"k": 15, "n1": 25, "n_unions": 40153992, "n_promising": 1192760, "tried": 1192760, "max_seeds": 32, "best_extras": 15, "best_total": 40, "found": false, "complete": true, "empty_by_part_count": false},
    "16": {"k": 16, "n1": 24, "n_unions": 101539605, "n_promising": 4349685, "tried": 4349685, "max_seeds": 33, "best_extras": 16, "best_total": 40, "found": false, "complete": true, "empty_by_part_count": false},
    "17": {"k": 17, "n1": 23, "n_unions": 239762280, "n_promising": 13307720, "tried": 13307720, "max_seeds": 35, "best_extras": 17, "best_total": 40, "found": false, "complete": true, "empty_by_part_count": false},
    "18": {"k": 18, "n1": 22, "n_unions": 528898200, "n_promising": 38532720, "tried": 38532720, "max_seeds": 40, "best_extras": 18, "best_total": 40, "found": false, "complete": true, "empty_by_part_count": false}
  },
  "found_41": false,
  "complete": true,
  "comment": "every seed-union with |U|<=maxk by canonical DFS; a 41-set needs |E|>=|U|+1 extras whose missed sets sit in U"
}