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The algorithm resembles algorithms by Tiernan and Tarjan, but is faster because it considers each edge at most twice between any one circuit and the next in the output sequence.},","pos":"YS5O2UANXCWRI3W7KMRKKK7OT7R6V3QDL4JS4DRLXM2EZUIPFALAC:708"}},{"Add":{"text":" doi = {10.1137/0204007},","pos":"YS5O2UANXCWRI3W7KMRKKK7OT7R6V3QDL4JS4DRLXM2EZUIPFALAC:740"}},{"Add":{"text":" eprint = {https://doi.org/10.1137/0204007},","pos":"YS5O2UANXCWRI3W7KMRKKK7OT7R6V3QDL4JS4DRLXM2EZUIPFALAC:788"}},{"Add":{"text":" url = {https://doi.org/10.1137/0204007},","pos":"YS5O2UANXCWRI3W7KMRKKK7OT7R6V3QDL4JS4DRLXM2EZUIPFALAC:836"}}]}},{"Edit":{"inode":{"change":4,"pos":7949},"path":"ch3_theory.tex","line":502,"atom":{"EdgeMap":{"edges":[{"previous":"BLOCK","flag":"BLOCK | DELETED","from":{"change":4,"pos":2943},"to":{"change":2,"start":0,"end":92},"introduced_by":2}],"inode":{"change":4,"pos":7949}}},"contents":[{"Del":{"text":">>>>>>> 1 [LOQBLRZ6 ]","pos":"M5WHUJXX7KNK425RXFM2U6WT3M4PARJFO7T7MLN2IBDEYDKPXTMAC:21"}},{"Del":{"text":"\\section{Abstraction}\\label{sec:abstraction}","pos":"M5WHUJXX7KNK425RXFM2U6WT3M4PARJFO7T7MLN2IBDEYDKPXTMAC:66"}},{"Del":{"text":"======= 1 [QIVGMR6I WIP]","pos":"M5WHUJXX7KNK425RXFM2U6WT3M4PARJFO7T7MLN2IBDEYDKPXTMAC:91"}}]}},{"Edit":{"inode":{"change":4,"pos":7949},"path":"ch3_theory.tex","line":1051,"atom":{"NewVertex":{"up_context":[{"change":4,"pos":4125}],"down_context":[{"change":4,"pos":6126}],"flag":"BLOCK","start":838,"end":1053,"inode":{"change":4,"pos":7949}}},"contents":[{"Add":{"text":"Finding loops in a program can be done with the algorithm described by","pos":"YS5O2UANXCWRI3W7KMRKKK7OT7R6V3QDL4JS4DRLXM2EZUIPFALAC:908"}},{"Add":{"text":"\\citeauthor{johnson1975}\\cite{johnson1975}. ","pos":"YS5O2UANXCWRI3W7KMRKKK7OT7R6V3QDL4JS4DRLXM2EZUIPFALAC:953"}},{"Add":{"text":"The algorithm is linear in the number of edges in the graph, specifically","pos":"YS5O2UANXCWRI3W7KMRKKK7OT7R6V3QDL4JS4DRLXM2EZUIPFALAC:1027"}},{"Add":{"text":"$\\mathcal{O}(n+e (c+1))$","pos":"YS5O2UANXCWRI3W7KMRKKK7OT7R6V3QDL4JS4DRLXM2EZUIPFALAC:1052"}}]}},{"Edit":{"inode":{"change":4,"pos":7949},"path":"ch3_theory.tex","line":1056,"atom":{"EdgeMap":{"edges":[{"previous":"BLOCK","flag":"BLOCK | DELETED","from":{"change":4,"pos":6168},"to":{"change":4,"start":6168,"end":6169},"introduced_by":4}],"inode":{"change":4,"pos":7949}}},"contents":[{"Del":{"text":"","pos":"6PTHERE26NXSC3ZXSI5UYKWTMPYZD4WMYFBJKZE3MRRTKC7MIU6QC:6168"}}]}},{"Replacement":{"inode":{"change":4,"pos":7949},"path":"ch3_theory.tex","line":1067,"ins":{"up_context":[{"change":4,"pos":6723}],"down_context":[{"change":4,"pos":6873}],"flag":"BLOCK","start":1054,"end":1238,"inode":{"change":4,"pos":7949}},"del":{"edges":[{"previous":"BLOCK","flag":"BLOCK | DELETED","from":{"change":4,"pos":6723},"to":{"change":4,"start":6723,"end":6873},"introduced_by":4}],"inode":{"change":4,"pos":7949}},"ins_contents":[{"Add":{"text":"Detecting all loops(cycles) in a graph can be done easily done with an ","pos":"YS5O2UANXCWRI3W7KMRKKK7OT7R6V3QDL4JS4DRLXM2EZUIPFALAC:1126"}},{"Add":{"text":"algorithm describe\\gls{dfs} on","pos":"YS5O2UANXCWRI3W7KMRKKK7OT7R6V3QDL4JS4DRLXM2EZUIPFALAC:1157"}},{"Add":{"text":"the graph. 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