[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/10887#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/10887","headline":"Hopcroft\u3068Karp -Wikipedia\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0","name":"Hopcroft\u3068Karp -Wikipedia\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0","description":"before-content-x4 Hopcroft\u3068Karp\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0 \uff081973\u5e74\u306bJohn E. Hopcroft\u3068Richard M. Karp\u306b\u3088\u3063\u3066\u958b\u767a\u3055\u308c\u307e\u3057\u305f\uff09\u306f\u3001\u30b0\u30e9\u30d5\u7406\u8ad6\u3067\u4f7f\u7528\u3055\u308c\u3001\u4e8c\u90e8\u306e\u6700\u5927\u306e\u30ab\u30fc\u30c7\u30a3\u30ca\u30ea\u30c6\u30a3\u3068\u306e\u30de\u30c3\u30c1\u30f3\u30b0\u3092\u6c7a\u5b9a\u3057\u307e\u3059\u3002\u305d\u308c\u306f\u30de\u30c3\u30c1\u30f3\u30b0\u304b\u3089\u629c\u3051\u51fa\u3057\u307e\u3059\u304c\u3001\u3053\u308c\u306b\u306f\u30a8\u30c3\u30b8\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u305b\u3093\u3002\u307e\u305f\u3001\u307e\u3060\u5bfe\u5fdc\u306e\u306a\u3044\u7d50\u3073\u76ee\u306e\u9593\u306b\u4ea4\u4e92\u306e\u30d1\u30b9\u3092\u69cb\u7bc9\u3057\u307e\u3059\u3002\u305d\u306e\u3088\u3046\u306a\u30d1\u30b9\u306f\u305d\u308c\u305e\u308c\u30011\u3064\u306e\u30a8\u30c3\u30b8\u306e\u5468\u308a\u306b\u4e00\u81f4\u3059\u308b\u62e1\u5927\uff08\u5897\u5f37\uff09\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002 after-content-x4 \u30a8\u30c3\u30b8\u306e\u30a8\u30c3\u30b8\u3092\u6301\u3064\u30b0\u30e9\u30d5\u3067\u3059 \u3068 {displaystyle e} \u30de\u30c3\u30c1\u30f3\u30b0 m \u2282 \u3068 {displaystyle msubset e} \u4e0e\u3048\u3089\u308c\u308b\u3068\u3001\u6728\u3067\u3042\u308b\u30b3\u30d2\u30fc\u30ec\u30f3\u30c8\u30b5\u30d6\u30b0\u30e9\u30d5\u3001\u3064\u307e\u308a\u30b5\u30a4\u30af\u30eb\u304c\u542b\u307e\u308c\u3066\u304a\u3089\u305a\u3001\u5b58\u5728\u3059\u308b\u3053\u3068\u3092\u691c\u8a0e\u3057\u3066\u304f\u3060\u3055\u3044","datePublished":"2023-12-11","dateModified":"2023-12-11","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/10887","wordCount":13914,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4 Hopcroft\u3068Karp\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0 \uff081973\u5e74\u306bJohn E. Hopcroft\u3068Richard M. Karp\u306b\u3088\u3063\u3066\u958b\u767a\u3055\u308c\u307e\u3057\u305f\uff09\u306f\u3001\u30b0\u30e9\u30d5\u7406\u8ad6\u3067\u4f7f\u7528\u3055\u308c\u3001\u4e8c\u90e8\u306e\u6700\u5927\u306e\u30ab\u30fc\u30c7\u30a3\u30ca\u30ea\u30c6\u30a3\u3068\u306e\u30de\u30c3\u30c1\u30f3\u30b0\u3092\u6c7a\u5b9a\u3057\u307e\u3059\u3002\u305d\u308c\u306f\u30de\u30c3\u30c1\u30f3\u30b0\u304b\u3089\u629c\u3051\u51fa\u3057\u307e\u3059\u304c\u3001\u3053\u308c\u306b\u306f\u30a8\u30c3\u30b8\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u305b\u3093\u3002\u307e\u305f\u3001\u307e\u3060\u5bfe\u5fdc\u306e\u306a\u3044\u7d50\u3073\u76ee\u306e\u9593\u306b\u4ea4\u4e92\u306e\u30d1\u30b9\u3092\u69cb\u7bc9\u3057\u307e\u3059\u3002\u305d\u306e\u3088\u3046\u306a\u30d1\u30b9\u306f\u305d\u308c\u305e\u308c\u30011\u3064\u306e\u30a8\u30c3\u30b8\u306e\u5468\u308a\u306b\u4e00\u81f4\u3059\u308b\u62e1\u5927\uff08\u5897\u5f37\uff09\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u30a8\u30c3\u30b8\u306e\u30a8\u30c3\u30b8\u3092\u6301\u3064\u30b0\u30e9\u30d5\u3067\u3059 \u3068 {displaystyle e} \u30de\u30c3\u30c1\u30f3\u30b0 m \u2282 \u3068 {displaystyle msubset e} \u4e0e\u3048\u3089\u308c\u308b\u3068\u3001\u6728\u3067\u3042\u308b\u30b3\u30d2\u30fc\u30ec\u30f3\u30c8\u30b5\u30d6\u30b0\u30e9\u30d5\u3001\u3064\u307e\u308a\u30b5\u30a4\u30af\u30eb\u304c\u542b\u307e\u308c\u3066\u304a\u3089\u305a\u3001\u5b58\u5728\u3059\u308b\u3053\u3068\u3092\u691c\u8a0e\u3057\u3066\u304f\u3060\u3055\u3044        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u672a\u6255\u3044\u306e\u7d50\u3073\u76ee\u3068\u3057\u3066 \u6839 \u3001 \u30c4\u30ea\u30fc\u5185\u306e\u6839\u304b\u3089\u5230\u9054\u3067\u304d\u308b\u30da\u30a2\u306e\u7d50\u3073\u76ee \u4ee3\u308f\u308a\u306e \u30b9\u30c8\u30ec\u30fc\u30c8\u30a8\u30c3\u30b8\u306e\u30d1\u30b9\u3002 \u4ea4\u4e92 \u30d1\u30b9\u306e\u30a8\u30c3\u30b8\u3082\u4ea4\u4e92\u306b\u884c\u3046\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059 m {displaystyle m} \u5c5e\u3057\u3001\u305d\u308c\u307b\u3069\u3067\u306f\u3042\u308a\u307e\u305b\u3093 m {displaystyle m} \u5c5e\u3059\u308b\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u308c\u3089\u306e\u30ce\u30c3\u30c8\u306f\u30eb\u30fc\u30c8\u304b\u3089\u307e\u3063\u3059\u3050\u3067\u3059\u3002 \u4ea4\u4e92\u306e\u30d1\u30b9\u306b\u6cbf\u3063\u305f\u3059\u3079\u3066\u306e\u30ce\u30c3\u30c8\u3068\u30a8\u30c3\u30b8\u3002\u3053\u308c\u306b\u306f\u3001\u30eb\u30fc\u30c8\u304b\u3089\u5947\u5999\u306a\u8ddd\u96e2\u3092\u6301\u3064\u30ce\u30fc\u30c9\u3082\u542b\u307e\u308c\u307e\u3059\u3002 \u4e00\u822c\u7684\u306a\u30ce\u30fc\u30c9\u3092\u6301\u3063\u3066\u3044\u306a\u3044\u305d\u306e\u3088\u3046\u306a\u6728\u306e\u91cf\u306f\u547c\u3073\u51fa\u3055\u308c\u307e\u3059 \u68ee \u3002 \u7d50\u3073\u76ee \u30d0\u30c4 {displaystyle x} \u3068 \u3068 {displaystyle y} \u68ee\u306e2\u3064\u306e\u7570\u306a\u308b\u6728\u304b\u3089\u3001\u305d\u308c\u305e\u308c\u304c\u6839\u304b\u3089\u307e\u3063\u3059\u3050\u306b\u3001\u7aef\u3092\u901a\u308a\u307e\u3059        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u30d0\u30c4 \u3068 \u2208 \u3068 {displaystyle xyin e} \u3053\u306e\u30a8\u30c3\u30b8\u3092\u63a5\u7d9a\u3067\u304d\u306a\u3044\u5834\u5408 m {displaystyle m} \u30ce\u30c3\u30c8\u306f\u3001\u3068\u306b\u304b\u304f\u5bfe\u5fdc\u3057\u3066\u3044\u306a\u3044\u30eb\u30fc\u30c8\u3067\u306a\u3044\u9650\u308a\u3001\u5225\u306e\u7aef\u3067\u30c4\u30ea\u30fc\u5185\u3067\u3059\u3067\u306b\u30da\u30a2\u306b\u306a\u3063\u3066\u3044\u308b\u305f\u3081\u3067\u3059\u3002\u30a8\u30c3\u30b8\u306e\u7aef\u306e\u3042\u308b\u30d1\u30b9 p {displaystyle p} 1\u3064\u306e\u6728\u306e\u6839\u5143\u304b\u3089 \u30d0\u30c4 \u3068 {displaystyle xy} \u4ed6\u306e\u30c4\u30ea\u30fc\u306e\u30eb\u30fc\u30c8\u306b\u306f\u3001\u5bfe\u5fdc\u306e\u306a\u3044\u30b9\u30bf\u30fc\u30c8\u3068\u30a8\u30f3\u30c9\u30ce\u30fc\u30c9\u306e\u3042\u308b\u4ea4\u4e92\u306e\u30d1\u30b9\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u306e\u3088\u3046\u306a\u9053\u306f\u306a\u308a\u307e\u3059 m {displaystyle m}  – \u30d1\u30b9\u3092\u7372\u5f97\u3057\u307e\u3059 \u306a\u305c\u306a\u3089\u3001\u306a\u305c\u306a\u3089 \uff08 m \u2216 p \uff09\uff09 \u222a \uff08 p \u2216 m \uff09\uff09 {displaystyle\uff08msetminus p\uff09\u30ab\u30c3\u30d7\uff08psetminus m\uff09} \u30a8\u30c3\u30b8\u3092\u542b\u3080\u30de\u30c3\u30c1\u30f3\u30b0\u3067\u3059 m {displaystyle m} \u3002 \u9006\u306b\u3001\u30de\u30c3\u30c1\u30f3\u30b0\u304c\u9069\u7528\u3055\u308c\u307e\u3059 m ‘ {displaystyle m ‘} \u305d\u308c\u306b\u306f\u3088\u308a\u591a\u304f\u306e\u30a8\u30c3\u30b8\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059 m {displaystyle m} \u3001\u30a8\u30c3\u30b8\u306e\u91cf\u306e\u30b5\u30d6\u30b0\u30e9\u30d5 \uff08 m \u2216 m ‘ \uff09\uff09 \u222a \uff08 m ‘ \u2216 m \uff09\uff09 {displaystyle\uff08msetminus m ‘\uff09cup\uff08m’setminus m\uff09} \u305d\u306e\u9593\u306e\u3059\u3079\u3066\u306e\u30d1\u30b9\u304c\u7d50\u679c\u3067\u3059 m {displaystyle m} \u3068 m ‘ {displaystyle m ‘} \u4ee3\u66ff\u3001\u305d\u3057\u3066\u5c11\u306a\u304f\u3068\u3082 | m ‘ |  –  | m | {displaystyle | m ‘|  –  | m |} \u9053 m {displaystyle m}  – \u81ea\u52d5\u5316\u306f\u76f8\u4e92\u30ce\u30fc\u30c9\u306a\u3057\u3067\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093\u3002 m {displaystyle m} \u3057\u305f\u304c\u3063\u3066\u3001\u4f55\u3082\u306a\u3044\u5834\u5408\u3001\u305d\u308c\u306f\u6700\u5927\u306e\u30de\u30c3\u30c1\u30f3\u30b0\u3067\u3059 m {displaystyle m}  – \u30d1\u30b9\u3092\u7372\u5f97\u3057\u307e\u3059\u3002 \u30cf\u30f3\u30ac\u30ea\u30fc\u306e\u68ee [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u691c\u8a0e\u4e2d\u306e\u68ee\u6797\u3092\u5b9a\u7fa9\u3059\u308b\u3068\u304d\u3001\u4e8c\u90e8\u30b0\u30e9\u30d5\u304c\u3042\u308b\u3068\u306f\u307e\u3060\u60f3\u5b9a\u3055\u308c\u3066\u3044\u307e\u305b\u3093\u3002\u4e8c\u90e8\u30b0\u30e9\u30d5\u3067 \uff08 \u306e \u222a \u306e \u3001 \u3068 \uff09\uff09 {displaystyle\uff08ucup v\u3001e\uff09} \u3057\u304b\u3057\u3001\u3055\u3089\u306b\u9069\u7528\u3055\u308c\u307e\u3059\uff1a\u305d\u3053\u306b\u306f\u3001\u306e\u30eb\u30fc\u30c8\u304b\u3089\u76f4\u63a5\u8ddd\u96e2\u304c\u3042\u308a\u307e\u3059 \u306e {displaystyleu} \u307e\u305f \u306e {displaystyle v} \u3001\u30eb\u30fc\u30c8\u304c\u3069\u3053\u306b\u3042\u308b\u304b\u306b\u5fdc\u3058\u3066\u3002\u68ee\u306b\u7d50\u3073\u76ee\u304c\u306a\u3044\u5834\u5408 \u30d0\u30c4 {displaystyle x} \u3068 \u3068 {displaystyle y} \u3068 \u30d0\u30c4 \u3068 \u2208 \u3068 {displaystyle xyin e} \u6700\u5f8c\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u306e\u3088\u3046\u306b\u3001\u68ee\u6797\u306f\u3001\u8a00\u53ca\u3055\u308c\u3066\u3044\u308b\u7279\u6027\u306b\u6e96\u62e0\u3057\u3066\u62e1\u5927\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u306a\u304f\u306a\u308a\u307e\u3057\u305f\u304c\u3001\u305d\u308c\u306f1\u3064\u3068\u547c\u3070\u308c\u3066\u3044\u307e\u3059 \u30cf\u30f3\u30ac\u30ea\u30fc\u306e\u68ee \u3002\u4e8c\u6975\u6027\u306e\u305f\u3081\u3001\u30cf\u30f3\u30ac\u30ea\u30fc\u306e\u68ee\u304c\u3042\u308b\u3068\u304d\u306b\u30de\u30c3\u30c1\u30f3\u30b0\u304c\u6700\u5927\u306e\u30de\u30c3\u30c1\u30f3\u30b0\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u6b21\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001Hopcroft\u3068Karp\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u4e88\u5099\u6bb5\u968e\u3067\u3059\u3002\u5f7c\u306f\u4e00\u81f4\u3057\u3066\u4e8c\u90e8\u30b0\u30e9\u30d5\u3092\u69cb\u7bc9\u3057\u307e\u3059 m {displaystyle m} \u8a00\u53ca\u3055\u308c\u305f\u30d7\u30ed\u30d1\u30c6\u30a3\u306e\u3042\u308b\u68ee\u3001\u305d\u308c \u68ee\u304b\u3089\u59cb\u3081\u307e\u3059\u3002\u68ee\u306f\u3001\u3059\u3079\u3066\u306e\u5bfe\u5fdc\u306e\u306a\u3044\u30ce\u30fc\u30c9\u3092\u6839\u3068\u3057\u3066\u542b\u307f\u307e\u3059\u304c\u3001\u30a8\u30c3\u30b8\u306f\u3042\u308a\u307e\u305b\u3093\u3002 \u7d50\u3073\u76ee\u306e\u7aef\u3092\u898b\u3064\u3051\u307e\u3059 \u30d0\u30c4 {displaystyle x} \u305d\u306e\u6839\u304b\u3089\u7d50\u3073\u76ee\u307e\u3067\u76f4\u63a5\u8ddd\u96e2\u306e\u3042\u308b\u68ee\u306e \u3068 {displaystyle y} \u68ee\u306b\u5c5e\u3057\u3066\u3044\u306a\u3044\u304b\u3001\u305d\u306e\u6839\u304b\u3089\u76f4\u63a5\u8ddd\u96e2\u3092\u6301\u3063\u3066\u3044\u308b\u4eba\u3002\u305d\u306e\u3088\u3046\u306a\u7d50\u3073\u76ee\u304c\u306a\u3051\u308c\u3070\u3001\u68ee\u306f\u30cf\u30f3\u30ac\u30ea\u30fc\u306e\u68ee\u3067\u3059\u3002\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u7d42\u4e86\u3057\u307e\u3059\u3002 \u6edd \u3068 {displaystyle y} \u305d\u306e\u6839\u304b\u3089\u30b3\u30a4\u30f3\u306b\u306f\u3001\u307e\u3063\u3059\u3050\u306a\u9577\u3055\u306e\u30ca\u30c3\u30c8\u306e\u9053\u304c\u3042\u308a\u307e\u3059\u3002 \u3068 {displaystyle with} \u5f8c \u3068 {displaystyle y} \u3002\u4e0e\u3048\u308b m {displaystyle m}  – \u306e\u30d1\u30b9\u3092\u7372\u5f97\u3057\u307e\u3059 \u30d0\u30c4 {displaystyle x} \u305d\u306e\u4e0a \u3068 {displaystyle y} \u5f8c \u3068 {displaystyle with} \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5f8c\u308d\u306b\u3057\u3066\u7d42\u4e86\u3057\u307e\u3059\u3002 \u6edd \u3068 {displaystyle y} \u68ee\u306e\u4e00\u90e8\u3067\u306f\u3042\u308a\u307e\u305b\u3093 \u3068 {displaystyle y} \u30da\u30a2\u30ea\u30f3\u30b0\u3001\u7d04 \u3068 \u3068 \u2208 m {displaystyle yzin m} \uff1a\u30ce\u30c3\u30c8\u3092\u8ffd\u52a0\u3057\u307e\u3059 \u3068 {displaystyle y} \u3068 \u3068 {displaystyle with} \u30a8\u30c3\u30b8\u3068\u540c\u69d8\u306b \u30d0\u30c4 \u3068 {displaystyle xy} \u3068 \u3068 \u3068 {displaystyle yz} \u68ee\u306b\u8ffd\u52a0\u3057\u3066\u3001\u30b9\u30c6\u30c3\u30d72\u306b\u623b\u308a\u307e\u3059\u3002 \u6700\u521d\u306b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0 m = \u2205 {displaystyle m = emptyset} \u5b9f\u884c\u3055\u308c\u305f\u3002\u5f7c\u304c\u30b9\u30c6\u30c3\u30d73\u306b\u3044\u308b\u5834\u5408 m {displaystyle m}  – \u30d1\u30b9\u3092\u7372\u5f97\u3057\u307e\u3059 p {displaystyle p} \u7d42\u308f\u308a\u3001\u610f\u5fd7 m {displaystyle m} \u7d42\u3048\u305f \uff08 m \u2216 p \uff09\uff09 \u222a \uff08 p \u2216 m \uff09\uff09 {displaystyle\uff08msetminus p\uff09\u30ab\u30c3\u30d7\uff08psetminus m\uff09} \u4ea4\u63db\u3059\u308b\u3068\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u518d\u5ea6\u5b9f\u884c\u3055\u308c\u307e\u3057\u305f\u3002\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u30b9\u30c6\u30c3\u30d72\u3067\u30cf\u30f3\u30ac\u30ea\u30fc\u306e\u68ee\u3067\u7d42\u308f\u308b\u5834\u5408\u3001\u6b21\u306b m {displaystyle m} \u6700\u65b0\u306e\u5f8c\u3001\u6700\u5927\u306e\u30de\u30c3\u30c1\u30f3\u30b0\u3067\u3059 \uff08 | \u306e | + | \u306e | \uff09\uff09 \/ 2 {displaystyle\uff08| u |+| v |\uff09\/2} \u4ed6\u306e\u30b1\u30fc\u30b9\u3067\u306f\u3001\u4e00\u81f4\u304c2\u30ce\u30c3\u30c8\u5897\u52a0\u3059\u308b\u305f\u3081\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u5168\u4f53\u304c\u767a\u751f\u3057\u307e\u3059\u3002\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e1\u56de\u306e\u5b9f\u88c5\u3092\u4f7f\u7528\u3057\u305f\u30e9\u30f3\u30bf\u30a4\u30e0\u306f\u3001\u30a8\u30c3\u30b8\u306e\u6570\u306b\u6bd4\u4f8b\u3057\u307e\u3059 | \u3068 | {displaystyle | e |} \u3001\u5b9f\u88c5\u304c\u7e70\u308a\u8fd4\u3055\u308c\u308b\u5408\u8a08\u9805\u306f\u3001\u30a8\u30c3\u30b8\u3068\u30ce\u30c3\u30c8\u306e\u6570\u306e\u7a4d\u306b\u6bd4\u4f8b\u3057\u307e\u3059\u3002 \u3053\u306e\u4f8b\u306e\u4e8c\u90e8\u30b0\u30e9\u30d5\u306b\u306f\u300110\u30ce\u30c3\u30c8\u306810\u306e\u30a8\u30c3\u30b8\u304c\u3042\u308a\u307e\u3059\u3002\u5de6\u5074\u3067\u306f\u3001\u3059\u3079\u3066\u306e\u30ce\u30c3\u30c8\u304c\u6700\u521d\u306e\u30d5\u30a7\u30fc\u30ba\u306e\u524d\u306b\u7121\u6599\u3067\u3001\u30de\u30c3\u30c1\u30f3\u30b0\u306f\u7a7a\u3067\u3059\u3002\u3059\u3079\u3066\u306e\u62e1\u5f35\u30d1\u30b9\u306f\u3001\u306e\u7d50\u3073\u76ee\u306e\u9593\u306e\u5358\u4e00\u306e\u7aef\u306b\u3042\u308a\u307e\u3059 \u306e {displaystyleu} \u3068\u7d50\u3073\u76ee \u306e {displaystyle v} \u524a\u6e1b\u3002\u305f\u3068\u3048\u3070\u3001\u5e45\u306e\u691c\u7d22\u3067\u30a8\u30c3\u30b8\u304c\u9078\u629e\u3055\u308c\u307e\u3059\u3002 \uff08 \u306e 0 \u3001 \u306e 0 \uff09\uff09 \u3001 \uff08 \u306e \u521d\u3081 \u3001 \u306e 4 \uff09\uff09 \u3001 \uff08 \u306e 2 \u3001 \u306e 2 \uff09\uff09 \u3001 \uff08 \u306e 4 \u3001 \u306e \u521d\u3081 \uff09\uff09 {displaystyle\uff08u_ {0}\u3001v_ {0}\uff09\u3001\uff08u_ {1}\u3001v_ {4}\uff09\u3001\uff08u_ {2}\u3001v_ {2}\uff09\u3001\uff08u_ {4}\u3001v_ {1}\uff09} \u7d50\u3073\u76ee\u3054\u3068\u306b \u306e {displaystyleu} \u81ea\u7531\u306a\u7d50\u3073\u76ee \u306e {displaystyle v} \u6700\u5c0f\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3067\u9078\u629e\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u91cf\u306e\u30d1\u30b9\u306f\u6700\u5927\u3067\u3042\u308a\u3001\u3059\u3079\u3066\u540c\u3058\u9577\u30551\u3001\u4fdd\u5b58\u3055\u308c\u305f\u30de\u30c3\u30c1\u30f3\u30b0\u306b\u306f\u30b5\u30a4\u30ba4\u30012\u3064\u306e\u30d5\u30ea\u30fc\u30ce\u30c3\u30c8\u304c\u6b8b\u308a\u30012\u3064\u306e\u30d5\u30ea\u30fc\u30ce\u30c3\u30c8\u304c\u6b8b\u308a\u307e\u3059\u3002 \u306e 3 {displaystyle u_ {3}} \u3068 \u306e 3 {displaystyle v_ {3}} \u3002 2\u756a\u76ee\u306e\u30d5\u30a7\u30fc\u30ba\u306f\u3001 \u306e {displaystyleu} \u307e\u305f\u306f\u306e\u552f\u4e00\u306e\u30d5\u30ea\u30fc\u30ce\u30fc\u30c9\u304b\u3089 \u306e {displaystyle v} \u898b\u3064\u3051\u308b\u306b\u306f\u3002\u6307\u5b9a\u3055\u308c\u305f\u30d1\u30b9 \uff08 \u306e 3 \u3001 \u306e 0 \u3001 \u306e 0 \u3001 \u306e \u521d\u3081 \u3001 \u306e 4 \u3001 \u306e 3 \uff09\uff09 {displaystyle\uff08u_ {3}\u3001v_ {0}\u3001u_ {0}\u3001v_ {1}\u3001u_ {4}\u3001v_ {3}\uff09} \u30de\u30c3\u30c1\u30f3\u30b0\u5185\u306e\u30de\u30c3\u30c1\u30f3\u30b0\u30a8\u30c3\u30b8\u3068\u8d64\u3044\u30a8\u30c3\u30b8\u306e\u5916\u5074\u306e\u9ed2\u3044\u30a8\u30c3\u30b8\u3092\u5207\u308a\u66ff\u3048\u307e\u3059\u3002\u5f7c\u306f\u9577\u30555\u306e\u9577\u3055\u3067\u3059\u3002\u9577\u30553\u306e\u30d1\u30b9\u306f\u306a\u3044\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u304c\u3001\u9577\u30557\u306e\u30d1\u30b9\u304c\u3042\u308a\u307e\u3059\u3002 \uff08 \u306e 3 \u3001 \u306e 4 \u3001 \u306e \u521d\u3081 \u3001 \u306e 0 \u3001 \u306e 0 \u3001 \u306e \u521d\u3081 \u3001 \u306e 4 \u3001 \u306e 3 \uff09\uff09 {displaystyle\uff08u_ {3}\u3001v_ {4}\u3001u_ {1}\u3001v_ {0}\u3001u_ {0}\u3001v_ {1}\u3001u_ {4}\u3001v_ {3}\uff09} \u3002\u9577\u30555\u306e\u30d1\u30b9\u3068\u306e\u4ee5\u524d\u306e\u30de\u30c3\u30c1\u30f3\u30b0\u306e\u5bfe\u79f0\u7684\u306a\u9055\u3044\u306b\u8d77\u56e0\u3059\u308b\u30de\u30c3\u30c1\u30f3\u30b0\u306f\u3001\u30b5\u30a4\u30ba5\u306e\u4f8b\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u81ea\u7531\u30ce\u30fc\u30c9\u304c\u3082\u3046\u306a\u3044\u305f\u3081\u306b\u6700\u5927\u3067\u3059\u3002 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5408\u8a08\u671f\u9593\u306f\u3001\u3044\u304f\u3064\u304b\u306e\u5834\u5408\u306b\u6e1b\u3089\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059 m {displaystyle m}  – \u30d1\u30b9\u3092\u540c\u6642\u306b\u8868\u793a\u3067\u304d\u307e\u3059\u3002\u305d\u3046\u3067\u3059 l \uff08 m \uff09\uff09 {displaystyle l\uff08m\uff09} \u6700\u77ed\u306e\u9577\u3055 m {displaystyle m}  – \u30d1\u30b9\u3092\u7372\u5f97\u3057\u307e\u3059\u3002\u79c1\u305f\u3061\u306f\u898b\u307e\u3059 m {displaystyle m} -Augmenting Knotty Junks Paths p \u521d\u3081 \u3001 … \u3001 p m {displaystyle p_ {1}\u3001ldots\u3001p_ {m}} \u9577\u3055 l \uff08 m \uff09\uff09 {displaystyle l\uff08m\uff09} \u3082\u3046\u8ab0\u3082 m {displaystyle m}  – \u9577\u3055\u306e\u7d4c\u8def l \uff08 m \uff09\uff09 {displaystyle l\uff08m\uff09} \u8ffd\u52a0\u3067\u304d\u307e\u3059\u3002\u305d\u306e\u5f8c\u3001\u305d\u308c\u3092\u793a\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059 "},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/10887#breadcrumbitem","name":"Hopcroft\u3068Karp -Wikipedia\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0"}}]}]