## Combinatorial Algorithms: T.C. Hu and M.T. ShingNewly enlarged, updated second edition of a valuable text presents algorithms for shortest paths, maximum flows, dynamic programming and backtracking. Also discusses binary trees, heuristic and near optimums, matrix multiplication, and NP-complete problems. 153 black-and-white illus. 23 tables. Newly enlarged, updated second edition of a valuable, widely used text presents algorithms for shortest paths, maximum flows, dynamic programming and backtracking. Also discussed are binary trees, heuristic and near optimums, matrix multiplication, and NP-complete problems. New to this edition: Chapter 9 shows how to mix known algorithms and create new ones, while Chapter 10 presents the "Chop-Sticks" algorithm, used to obtain all minimum cuts in an undirected network without applying traditional maximum flow techniques. This algorithm has led to the new mathematical specialty of network algebra. The text assumes no background in linear programming or advanced data structure, and most of the material is suitable for undergraduates. 153 black-and-white illus. 23 tables. Exercises, with answers at the ends of chapters. |

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### Contents

I | 1 |

III | 3 |

IV | 10 |

V | 17 |

VI | 23 |

VII | 24 |

VIII | 27 |

IX | 30 |

XXXV | 240 |

XXXVII | 241 |

XXXVIII | 242 |

XXXIX | 254 |

XL | 273 |

XLII | 275 |

XLIII | 278 |

XLIV | 279 |

X | 40 |

XII | 46 |

XIII | 60 |

XIV | 83 |

XV | 86 |

XVI | 107 |

XVIII | 121 |

XIX | 132 |

XX | 138 |

XXII | 145 |

XXIII | 147 |

XXIV | 151 |

XXV | 162 |

XXVII | 171 |

XXVIII | 173 |

XXIX | 180 |

XXX | 188 |

XXXI | 191 |

XXXII | 195 |

XXXIII | 222 |

XXXIV | 228 |

XLV | 282 |

XLVI | 288 |

XLVIII | 291 |

XLIX | 293 |

L | 300 |

LII | 304 |

LIII | 305 |

LIV | 308 |

LV | 314 |

LVI | 320 |

LVII | 326 |

LVIII | 329 |

LIX | 331 |

LX | 337 |

LXI | 340 |

LXIII | 341 |

LXIV | 342 |

LXV | 346 |

LXVI | 348 |

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### Common terms and phrases

adjacent arc capacities arc flow assume augmenting path backtrack binary tree called Chapter circular nodes compatible pair computation connected consider construct convex polygon corresponding cost cut separating decision tree define denote dynamic programming error ratio example extended binary tree Fk(y Fk+j(y flow-augmenting path GH tree graph greedy algorithm heuristic algorithm host host-feasible circle Hu-Tucker algorithm Huffman indexed set integers intermediate nodes knapsack problem layer Lemma matrix maximum flow values minimum cut minimum spanning tree n-gon neighbors network degree Network Flows node Vj Note NP-complete optimality optimum partition optimum solution pairs of nodes phase polygon polynomial preflow Prim's algorithm Proof represent satisfy shortest distance shortest path shortest path problem shown in Figure solved square nodes Step subpath subpolygon subset subtree T. C. Hu temporary label terminal nodes Theorem tree edge triple operations vector