zui4 xiao3 xiang1 jiao1 lu4 jing4 han2 shu4 (MinimalCutSetFn)

A UnaryFunction that assigns a Graph the Class of GraphPaths which comprise cutsets for the Graph and which have the least number of GraphArcs.

Ontology

SUMO / GRAPH-THEORY

Class(es)

zhong3 lei4

ke3 ji4 cheng2 guan1 xi4

yi1 yuan2 han2 shu4

zui4 xiao3 xiang1 jiao1 lu4 jing4 han2 shu4

Coordinate term(s)

jue2 dui4 zhi2 han2 shu4 miao2 shu4 han2 shu4 hu2 yu2 xian2 hu2 zheng4 xian2 hu2 zheng4 qie1 fan3 mian4 han2 shu4 shi2 jian1 kai1 shi3 han2 shu4 zui4 chu1 jie2 dian3 han2 shu4 ji4 shu4 han2 shu4 shang4 xian4 han2 shu4 hu4 bu3 han2 shu4 yu2 xian2 han2 shu4 xiang1 jiao1 lu4 jing4 han2 shu4 dan1 wei4 han2 shu4 shi2 jian1 jie2 shu4 han2 shi4 zui4 hou4 jie2 dian3 han2 shu4 fan4 wei2 han2 shu4 xia4 xian4 han2 shu4 zheng4 mian4 han2 shu4 shi2 jian1 wei4 lai2 han2 shi4 gai4 hua4 han2 shu4 gai4 hua4 lian2 ji2 han2 shu4 shi2 yi4 ji4 han2 shu4 xu1 shu4 han2 shu4 zui4 jin4 wei4 lai2 shi2 jian1 han2 shu4 zui4 jin4 guo4 qu4 shi2 jian1 han2 shu4 qi3 shi3 jie2 dian3 han2 shu4 zheng3 shu4 ping2 fang1 gen1 han2 shu4 qian1 ji4 han2 shu4 lie4 zhang3 han2 shu4 ji2 shu4 han2 shu4 bai3 wan4 ji4 han2 shu4 bai3 wan4 fen1 zhi1 yi1 ji4 han2 shu4 qian1 fen1 zhi1 yi1 ji4 han2 shu4 nai4 mi3 han2 shu4 fen1 zi3 han2 shu4 zu3 zhi1 han2 shu4 guo4 qu4 shi2 jian1 han2 shi4 lu4 jing4 liang4 han2 shu4 zhao4 fen1 zhi1 yi1 ji4 han2 shu4 mi4 ji2 he2 han2 shu4 qian2 shu4 han2 shu4 zhu3 ti1 han2 shu4 huo4 ran2 lv4 han2 shu4 te4 xing4 han2 shu4 you3 li3 shu4 han2 shu4 shi2 shu4 han2 shu4 dao3 shu4 han2 shu4 zheng3 shu4 han2 shu4 zheng4 fu4 hao4 han2 shu4 zheng4 xian2 han2 shu4 biao3 pi2 han2 shu4 ping2 fang1 gen1 han2 shu4 hou4 shu4 han2 shu4 zheng4 qie1 han2 shu4 zhao4 ji4 han2 shu4 zhong1 jie2 dian3 han2 shu4 cai2 chan3 han2 shu4 cun2 zai4 shi2 jian1 han2 shu4 nian2 fen4 han2 shu4

Type restrictions

subclass tu2 lu4 jing4 MinimalCutSetFn(tu2)

Axioms (4)

zui4 xiao3 xiang1 jiao1 lu4 jing4 han2 shu4 na4 bu4 xiang1 guan1 yu1 xiang1 jiao1 lu4 jing4 han2 shu4.

(relatedInternalConcept MinimalCutSetFn CutSetFn)

If graph shi4 tu2 de5 shi2 li4, then "hua2 fen1 graph wei2 liang3 du2 li4 tu2 biao3 de5 zui4 xiao3 xiang1 jiao1 lu4 jing4" shi4 "hua2 fen1 graph wei2 liang3 du2 li4 tu2 biao3 de5 xiang1 jiao1 lu4 jing4" de5 ci4 zhong3 lei4.

(=>
      (instance ?GRAPH Graph)
      (subclass
            (MinimalCutSetFn ?GRAPH)
            (CutSetFn ?GRAPH)))

if "hua2 fen1 graph wei2 liang3 du2 li4 tu2 biao3 de5 zui4 xiao3 xiang1 jiao1 lu4 jing4" deng3 yu1 pathclass,
then there exists number so_that_not for all path holds: if path shi4 pathclass de5 shi2 li4, then path de5 lu4 jing4 chang2 shi4 number

(=>
      (equal
            (MinimalCutSetFn ?GRAPH)
            ?PATHCLASS)
      (exists
            (?NUMBER)
            (forall
                  (?PATH)
                  (=>
                        (instance ?PATH ?PATHCLASS)
                        (pathLength ?PATH ?NUMBER)))))

There don't exist hua2 fen1 graph wei2 liang3 du2 li4 tu2 biao3 de5 xiang1 jiao1 lu4 jing4 path1,hua2 fen1 graph wei2 liang3 du2 li4 tu2 biao3 de5 zui4 xiao3 xiang1 jiao1 lu4 jing4 path2 so_that_not path1 de5 lu4 jing4 chang2 shi4 number1 and path2 de5 lu4 jing4 chang2 shi4 number2 and number1 xiao3 yu1 number2.

(not
      (exists
            (?PATH1 ?PATH2)
            (and
                  (instance
                        ?PATH1
                        (CutSetFn ?GRAPH))
                  (instance
                        ?PATH2
                        (MinimalCutSetFn ?GRAPH))
                  (pathLength ?PATH1 ?NUMBER1)
                  (pathLength ?PATH2 ?NUMBER2)
                  (lessThan ?NUMBER1 ?NUMBER2))))