Posted: December 30th, 2021
{ti points} Let G = (HE) he a cermected, undirected graph. [In this ceurse wefellmu the usualcenverltierl that, unless indicated UH’IEI’WiSE, an undirected graph dues net have loops er multipleedgesj?susualn = |V| andm= |E|. Art urticaria-tier: paint of G is a vertex whese remeval discerlnects G.Aswesawinclass,iiyeurunDFSmG,then{hecauseGiscermected}theeuterreutinewillhavetemalte enl}r one call Exp]ere{G,r} fer some vertex r, after whim all verlices will he visited.The“tree”edgesereatedin?iispreeessfermasparmingteeTefGreetedatr. {a} Prm’e?tatrisanarlicula?enpeintifandenlyifithasatleasttwechildrenin’l”. {b} Lettraér.Theancestersefeare?reve?icesenthesimplepathinTiremeter?nelusive.Praperancestersext?udes.Thedescendantsefearethesewhidthaveuasanancester. Prm’e?iatuisanarlict?atienpeintiiander?yif?iereisachildseiein T.sud1thatnedescendantefshasahackedgetnapreperancesterefu. {c} Let lew [u] = min{pre[w} : El descendant 1.: iii tr such that (u, w] is a back edge}. Shaw hmte cmnpute all lm?u} in time DEM}. {:1} Show haw te cempute all arliculaticrrl points in time DEM}.Runtimes in this problem are in the ward model (baelc arithmetic etc. is in unit time}.
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