{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lec0502-MST-ann - DIS'I’INWISIIED LECTURE SIRIES c All...

Info icon This preview shows pages 1–14. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
Image of page 7

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 8
Image of page 9

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 10
Image of page 11

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 12
Image of page 13

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 14
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: DIS'I’INWISIIED LECTURE SIRIES c All m“ V - MAY 2-3. 2011 '_:_-_' u 7.4 ”gnu. :l“ u. ",5. ‘ 1 ”v.4 Monday, May 2. 4 pm in 1404 Siebel Center Natural Language Applications Across Genres: From News to Novels Prof. Kathleen McKeown. Columbia University Monday, May 2, 6 pm In 2405 Slebel Center Attending Graduate School: A panel discussion Tuesday, May 3. 10 am 2405 Slebel Center Machine Learning - Modern Times Dr Corinna Cortes (Head of Google Research, NY) Announcements: MP 7 available. Due 5/4. 11:59p. “Ml ‘h'.1"o, Algorithms - MST Graphs: Traversal - quiz Aloudtttm (Ox): . VISITED) WHO NEW) p-__(V) For al w In G. _(V) II MW) - WEXPLORED m(v.w).msoovenv) MW. VISITEO) 9—0”) Oh. I M030) - UNEXPLCXIED M(v.w).—) Running time: If we do not assume an Increases to . Why? implementation. the running time Minimum Spanning Tree Algorithms: -input: connected. undirected graph G with unconstrained edge weights oOutput: a graph G' with the following characteristics - 06' is a spanning subgraph of G -G' is connected and acyclic (a tree) -6' has minimal total weight among all such spanning trees - Kruskal‘s Algofithm mmmmmmmmmmmmmmmfi Kruskal's Algorithm (1956) oat/at. Let :t Consost of all n VerzflCes and no edges. 2. bmtIa/IZQ a div/out Jet‘s Structure where each Vertex is represented 4/ a Set. —a-> “new!“ from P4 mm W, add the edge to Tam! taée duo» of the VertICes taco Jets, cat/venous: do not/rug (eyed ado/ A4...— edges are added to 7‘. 3 m m m m m m m m m m m m m m N“ ". K ‘7, V? Algorithm KWSTIG) Kruskal's Algorithm - preanalysls disjolnLS'etsforrsl: for each vertex v In Vdo forestmakeSeuv): for! near Q. rL-sel‘te eges into Q. keyed by weights graph 1' - (ME) with E - a: while 1' has fewer than 0-! edges do edge e - QwenmwMino Let u. v be the end ints oft- If oust. m! v :- Eamaaudluz then gfflfl cgfl'e :1 to or Union 0“) éfimatfiumv’fmuflnflu» return 1' Priority Sorted I re, 5 1' ad '9 —l-:mlmcm , °3 ‘ "3" ' .15. -gifi Ahorltllm KruskclMSTlG) disjointSem forest: 0‘ .3 for each vertex v in Vdo 0( \ faresamakeSedv): n mag-mam by waste ' graph r - ms) with E - a.- 06!“ while Thas fewer than n-l edges do edge e - ernmveMin Let u. v be I f c lfforcsaflmflv) :- or:st.flnd(u) then Add edge e to forest. smartUnion (forestfinflwfmstfindmfi Kruskal's Algorithm - analysis Prim's algorithms (1957) is based on the Partition Property: Consider a partition of the vertices of 6 Into subsets U and V. Let e be an edge of minimum weight across the partition. Then e is part of some minimum spanning tree. Proof: See (3473 .—? Example of Prim's algorithm - Example of Prim's algorithm - Fat II v. dlv] = flnfinly'. . lulu-In. source: dls] = 0 lnlllalln priority (R) quoooJI']| lnlllallusotoflabolodvonlcabe. Fat II unlabelled neighbors w of v. If oost(v.w) < dlw] dlw] I coct(v.w) PM = V MW ‘ELW‘ Prim’s Algorithm (momma graph wlth ammo v - . Initialize structure: ' 1. For II V. dlv] = "lnllnlty'. pM = nul mil 2. mum m: an] x 0 Cl 0 3. hltlnllze pdorlty (min) queudn)lt 0 n 4. hummduwvmmaot Repeat these steps n times: - mmszrmsmam 2. Lebelvettexv(setel|eg) ob) >For el unlabelled nelglbon w of v. If ooet(v.w) < dlw] ptw] = v Prim's Algorithm (momma graph wan unconstrained edge mm): Initialize structure: 1 . For al v. dlv] = "Infinity'. 9M = ml 2. “who am: dls] I 0 3. hid-liz- ptlomy (min) queue 4. hummdhbdodmba Repeat those steps n times: 1. Find minimum dll "WW m” V Which is best? Depends a» density of the W”: Spa-5c 3. For-lunhbollodndgtbonwofv. 1' : 2. Labelqu I‘ eastern) < dlw] dlw] 8 ooct(v.w) 9M = v ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern