Tunable Survivable Spanning Trees Jose Yallouz, Ori Rottenstreich and Ariel Orda
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1 Tble Svvble Spg Tees Jse Yllz, O Reseh d Ael Od Depe f Elel Egeeg Teh, Isel Ise f Tehlgy T ppe Peedgs f ACM Sges 2014
2 Qly f Seve (QS) The Iee ws develped s Bes Eff ewk. Wh s Qly f Seve (QS)? The lleve effe f seve pefe whh deees he degee f se ssf f he seve. (ITU) I d QS e: Dely Pke lss Je O f de Bdwdh Svvbly QS e lssf: Bleek Addve 2
3 Svvbly Svvbly The pbly f he ewk seve y he pesee f fles. Revey Shees Res s ps-fle pel pess,.e. bkp sl s lled ly fe he fle ee. Typl evey es ge f seds es. Pe s pe-fle plg pess,.e. bkp sl s lled dve befe he fle ee. Typl evey es e he ge f llseds. Adg y sdds, sgle fle evey pe s be pefed wh 50 s. These w ehqes e fe pleeed gehe. Fs Fle Pe, Nex Fles Res I d 3
4 Sgle fle Mdel Sgle Fle Mdel: sses h s e fle be hdled he ewk Ude he sgle lk fle del, ly he lks h e ll phs fl he e. I d lk 4
5 Bdsg ehds Bdsg - ehd f sfeg essge ll epes slesly. v Spg-Tee Bds Fldg Bds 5
6 Tble svvbly Fll svvbly - (100%) pe gs ewk sgle fles. Esblshe f lk-dsj spg ees. Ths shee s fe esve. v lk S=0.99 p e =0.01 Tble svvbly llws y desed degee f svvbly he ge 0% 100%. 6
7 Mdel Fl Newk epeseed by deed gph, G(V, E) b e : bdwdh f lk e p e : fle pbbly f lk e Gve ewk G V, E, k-svvble spg e s ple f k spg ees (T 1,, T k ) ( eessly dsj). f l T 1, T 2 2-svvble spg e T 1 T 2 7
8 Mdel Fl The svvbly level f (T 1,, T k ) s defed s: The pbbly h ll lks e pel S(T 1,, T k ) = 1 ( k =1 T k = ) e k =1 T k 1 p e k ( =1 T k ) S T 1, T 2 = = (0. 99) f l T 1 T 2 8
9 Mdel Fl The bdwdh f (T 1,, T k ) s defed: The bdwdh f he bleek lk ss ll spg ees. B(T 1,, T k ) = e B T 1, T 2 = 2 k =1 Tk {b e } S T 1, T 2 = f l T 1 T 2 9
10 Opz Pbles Csed Bdwdh Mx-Svvbly (CBMS) Pble: Fd k-svvble spg e (T 1,, T k ) sh h: x S(T 1,, T k ) B(T 1,, T k ) B 0 p z Csed Svvbly Mx-Bdwdh (CSMB) Pble: Fd k-svvble spg e (T 1,, T k ) sh h: x B(T 1,, T k ) S(T 1,, T k ) S 0 10
11 Hw My Spg Tees? Eplyg e spg ees gh ese he svvbly level. S T 1, T 2, T 3 T 1 = 1 S T 1, T 2 = h e z T 2 T 3 11 Hweve, e spg ees pse hghe gee vehed.
12 Hw My Spg Tees? h e z 12
13 Hw My Spg Tees? V = 5 E E V + 1 = = 2 h e z 13
14 Algh Shee Csed Bdwdh Mx-Svvbly (CBMS) Pble: Fd k-svvble spg e (T 1,, T k ) sh h: x S(T 1,, T k ) B(T 1,, T k ) B 0 M Cs Edge Dsj Spg Tee Pble: Gve deed weghed ewk G(V,E). Fd k Edge Dsj Spg Tees (T 1,, T k ) f l l s. w e e Plyl sl by Rskd d Tj A e fdg -s edge-dsj spg ees, k =1 T k A l g h s l 14
15 Algh f he CBMS Pble Esblshg k-svvble spg e Gph sf: F eh lk e wh bdwdh b e < B 0 b e, p e F eh lk e wh bdwdh b e B 0 b e, p e Dsd he lk w e1 = l(1 p e ) w e2 = 0 w ek = 0 Fd k Edge Dsj Spg Tees dg s edge dsj spg ee lgh. A l g h s l 15
16 Sl s l Mx svvbly level vess he be f spg ees k f dffee bdwdh eqees k 16
17 Sl s l X12 es pvee Bdwdh vess he svvbly level eqee S 0 17
18 Cls The esblshe f pehesve ehdlgy f effely pvdg ble svvbly. R Be d Ael Od. The pwe f g: A vel pph f he effe desg f svvble ewks. I IEEE/ACM Ts. Newkg, Jse Yllz d Ael Od. Tble QS-we ewk svvbly. I IEEE If, Jse Yllz, O Reseh d Ael Od. Tble Svvble Spg Tees. T ppe ACM Sges,
19 19
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