L18-shortestPaths

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Unformatted text preview: f 6 h b a c b a c b a c shortest paths b 8 d 8 g 10 a 2 e 9 3 12 c 5 9 11 3 1 i f 6 h image:www.princegeorgeva.org, thefranciscofamily.org, www.rightdriveacademy.co.uk, www.ccscambridge.org, www.drawingcoach.com, www.pastoral.org.uk, www.daasgallery.com what about negative edge weights? where does old argument break down first ideas: sssp(G,s) shorti,v = sssp(G,s) shorti,v 8 >1 > < 0 = > > minx2V : i=0 v=s ⇢ shorti shorti 1,v 1,x + w(x, v ) max len of a simple path: bellman-ford(G,s) bellman-ford(G, s) 1 short0,s ⇥ 0 2 ⇧v ⌅ V {s}, short0,v ⇥ ⇤ 3 for i = 1, . . . , V 1 4 do for each v ⌅ V {s} 5 do shorti,v = minx⇥Adj (v) shorti 1,v w(x, v ) + shorti 1,x ⇥ 4 5 do for each v ⌅ V {s} do shorti,v = minx⇥Adj (v) shorti 1,v w(x, v ) + shorti bellman-ford(G, s) 1 short0,s ⇥ 0 2 ⇧v ⌅ V {s}, short0,v ⇥ ⇤ 3 for i = 1, . . . , V 1 4 do for each e = (x, y ) ⌅ E ⇤ ⌥ shorti 1,y shorti,y 5 do shorti,y = min ⇧ w(x, y ) + shorti 1,x ⌅ ⌃ 1,x ⇥ b 8 d 3 -12 9 i=0 v=s ⇢ shorti shorti i 5 -4 -3 c shorti,v 2 e -4 8 >1 > < 0 = > > minx2V : g 7 10 a 5 1 1,v 1,x + w(x, v ) f 6 h a b c d0 e f g h i 0 1 2 bf(G,d) 3 4 5 6 7 b 8 d 3 -12 9 i=0 v=s ⇢ shorti shorti i 5 -4 -3 c shorti,v 2 e -4 8 >1 > < 0 = > > minx2V : g 7 10 a 5 1 1,v 1,x + w(x, v ) f 6 h a b c d0 e f g h...
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This note was uploaded on 02/25/2014 for the course CS 4102 taught by Professor Horton during the Spring '10 term at UVA.

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