LEO VAN IERSEL TU DELFT

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Transcription:

LEO VAN IERSEL TU DELFT

UT LEO VAN IERSEL TU DELFT

UT LEO VAN IERSEL TU DELFT TU/

CWI UT LEO VAN IERSEL TU DELFT TU/

CWI UT TUD LEO VAN IERSEL TU DELFT TU/

Tnzni & Kny yr LEO VAN IERSEL TU DELFT Nw Zln.5 yrs

Dfinition Lt X finit st. A (root) phylognti tr on X is root tr with no ingr- outgr- vrtis whos lvs r ijtivly lll y th lmnts of X. 82 My 76 My 68 My 35 My Kiwi (Nw Zln) Cssowry (Nw Guin + Austrli) Lo vn Irsl (TUD) Emu (Austrli) Ostrih Mo (Afri) (Nw Zln) Introuing nw ollgus 3TU.AMI 8 mr 205 /

Lo vn Irsl (TUD) Introuing nw ollgus 3TU.AMI 8 mr 205 2 /

Lo vn Irsl (TUD) Introuing nw ollgus 3TU.AMI 8 mr 205 3 /

W.F. Doolittl t l. (2000) Lo vn Irsl (TUD) Introuing nw ollgus 3TU.AMI 8 mr 205 4 /

Dfinition Lt X finit st. A (root) phylognti ntwork on X is root irt yli grph with no ingr- outgr- vrtis whos lvs r ijtivly lll y th lmnts of X. Lo vn Irsl (TUD) Introuing nw ollgus 3TU.AMI 8 mr 205 5 /

Th first phylognti ntwork (Buffon, 755) Lo vn Irsl (TUD) Introuing nw ollgus 3TU.AMI 8 mr 205 6 /

Mrussn t l., Anint hyriiztions mong th nstrl gnoms of r wht. Sin (204) Lo vn Irsl (TUD) Introuing nw ollgus 3TU.AMI 8 mr 205 7 /

Origin of tropil pthogn C. gttii tr to th Amzon Hgn t l., Anint isprsl of th humn fungl pthogn Cryptoous gttii from th Amzon rinforst. PLoS ONE (203). Lo vn Irsl (TUD) Introuing nw ollgus 3TU.AMI 8 mr 205 8 /

PART : NETWORKS FROM TREES Spis Spis Spis Spis Spis ACCCTAG--TC-ATC---AGC-GAC-C ATACTAGTTTT-ATC-AAAGC-GAC-C ATATTAG-TC-GATCTACAGCTGAC-C ACCCTAGTTTCGGATCCAAGC-GAC-C ACC--TG-TCC-ATCTATG-CTGACTC TA-GTATCCCTC---TCTATATAT TA-GTAC---TCGGATCT--ATAT TAGGTACCCCTCGGATCCATAT-T TA-GTATCCCTC---TCTATATCT TA-GTATCCCTCAGA-CTATAT-A Gn trs Spis ntwork Lo vn Irsl (TUD) Introuing nw ollgus 3TU.AMI 8 mr 205 9 /

PART 2: NETWORKS FROM SUBNETS Spis Spis Spis Spis Spis ACCCTAG--TC--ATC---AGC-GAC-CTA-GTACCCTC---TCTATATAT ATACTAGTTTT--ATC-AAAGC-GAC-CTA-GTA---TCGGATCT--ATAT ATATTAG--TC-GATCTACAGC-GAC-CTAGGTACCCTCGGATCCATAT-T ACCCTAGTTTCGGATCCCAAGC-GAC-CTA-GTACCCTC---TCTATATCT ACC--TG--TCC-ATCT--AGC-GAC-CTA-GTACCCTCAGA-CTATAT-A Trints Spis ntwork Lo vn Irsl (TUD) Introuing nw ollgus 3TU.AMI 8 mr 205 0 /

PART 3: NETWORKS FROM SEQUENCES Spis Spis Spis Spis Spis ACCCTAG--TC--ATC---AGC-GAC-CTA-GTACCCTC---TCTATATAT ATACTAGTTTT--ATC-AAAGC-GAC-CTA-GTA---TCGGATCT--ATAT ATATTAG--TC-GATCTACAGC-GAC-CTAGGTACCCTCGGATCCATAT-T ACCCTAGTTTCGGATCCCAAGC-GAC-CTA-GTACCCTC---TCTATATCT ACC--TG--TCC-ATCT--AGC-GAC-CTA-GTACCCTCAGA-CTATAT-A Spis ntwork Lo vn Irsl (TUD) Introuing nw ollgus 3TU.AMI 8 mr 205 /

PART : NETWORKS FROM TREES

Tr-s Ntwork Ronstrution

Tr-s Ntwork Ronstrution

Tr-s Ntwork Ronstrution

Tr-s Ntwork Ronstrution

Tr-s Ntwork Ronstrution

Tr-s Ntwork Ronstrution

Noninry Trs Dfinition. A phylognti tr T is isply y phylognti ntwork N if T n otin from sugrph of N y ontrting gs.

Noninry Trs Dfinition. A phylognti tr T is isply y phylognti ntwork N if T n otin from sugrph of N y ontrting gs.

Noninry Trs Dfinition. A phylognti tr T is isply y phylognti ntwork N if T n otin from sugrph of N y ontrting gs.

Noninry Trs Dfinition. A phylognti tr T is isply y phylognti ntwork N if T n otin from sugrph of N y ontrting gs.

Tr-s Ntwork Ronstrution Hyriiztion numr: #gs to ut to otin tr

Rsults Prolm: HYBRIDIZATION NUMBER Givn: Colltion of phylognti trs T, h on th sm n lvs, k N Qustion: Dos thr xist phylognti ntwork tht isplys h tr in T n hs hyriiztion numr t most k? Two inry trs: Dirt rltionship to mximum yli grmnt forst (MAAF) O((28k)k + n3 )-tim lgorithm (Borwih & Smpl 2007) O(3.8k n)- tim lgorithm (Whin, Biko & Zh, 203) Sm pproximility s irt fk vrtx st (Klk, vi, Lki, Linz, Sornv, Stougi, 202) Any numr of noninry trs: (vi, Klk & Sornv, 204) Krnl with 4k(5k) t lvs, with t th numr of trs Krnl with 20k2 ( + ) lvs, with + th mximum outgr n f (k) t-tim oun-srh lgorithm, with f stronomil Thr inry trs: k poly(n) tim lgorithm (vi, Lki, Klk, Whin & Zh, 204) ( = 60989840)

Rsults Prolm: HYBRIDIZATION NUMBER Givn: Colltion of phylognti trs T, h on th sm n lvs, k N Qustion: Dos thr xist phylognti ntwork tht isplys h tr in T n hs hyriiztion numr t most k? Two inry trs: Dirt rltionship to mximum yli grmnt forst (MAAF) O((28k)k + n3 )-tim lgorithm (Borwih & Smpl 2007) O(3.8k n)- tim lgorithm (Whin, Biko & Zh, 203) Sm pproximility s irt fk vrtx st (Klk, vi, Lki, Linz, Sornv, Stougi, 202) Any numr of noninry trs: (vi, Klk & Sornv, 204) Krnl with 4k(5k) t lvs, with t th numr of trs Krnl with 20k2 ( + ) lvs, with + th mximum outgr n f (k) t-tim oun-srh lgorithm, with f stronomil Thr inry trs: k poly(n) tim lgorithm (vi, Lki, Klk, Whin & Zh, 204) ( = 60989840)

Agrmnt Forsts An grmnt forst of two inry trs is forst tht n otin from ithr tr y lting gs n unlll vrtis n supprssing ingr- outgr- vrtis T T2

Agrmnt Forsts An grmnt forst of two inry trs is forst tht n otin from ithr tr y lting gs n unlll vrtis n supprssing ingr- outgr- vrtis T T2 Inhritn Grph An grmnt forst is yli if its inhritn grph is yli An yli grmnt forst with minimum numr of omponnts is ll Mximum Ayli Agrmnt Forst (MAAF)

Agrmnt Forsts An grmnt forst of two inry trs is forst tht n otin from ithr tr y lting gs n unlll vrtis n supprssing ingr- outgr- vrtis T T2 Inhritn Grph An grmnt forst is yli if its inhritn grph is yli An yli grmnt forst with minimum numr of omponnts is ll Mximum Ayli Agrmnt Forst (MAAF) For two inry trs: HYBRIDIZATION NUMBER = MAAF - (Borwih & Smpl 2007)

Agrmnt Forsts vs Hyriiztion Ntworks T T2 Inhritn Grph

Agrmnt Forsts vs Hyriiztion Ntworks T T2 Inhritn Grph

Agrmnt Forsts vs Hyriiztion Ntworks T T2 Inhritn Grph

Agrmnt Forsts vs Hyriiztion Ntworks T T2 Inhritn Grph

Agrmnt Forsts vs Hyriiztion Ntworks T T2 Dltion AAF

Hyriiztion Numr on thr trs in k poly(n) tim

Hyriiztion Numr on thr trs in k poly(n) tim Dltion AAF Thr trs: HYBRIDIZATION NUMBER MAAF -

Hyriiztion Numr on thr trs in k poly(n) tim Dltion AAF Thr trs: HYBRIDIZATION NUMBER MAAF -

Invisil Componnts n th Extn AAF v v, v2 v4 v2 v3 v3 v4

Four Trs My Not Hv n Optiml Cnonil Ntwork

Rution Ruls i j hi gh fg k lm no j m h no k l g f f j i klm no

Rution Ruls i j hi gh fg k lm no j m h no k l g f i klm no f j m no k l Common pnnt sutr

Rution Ruls i j hi x g h x j h fg g f i f j Ru sutr to singl lf x

Rution Ruls i j x hi x g h j h fg g f f j g f Common hin i x

Rution Ruls i j hi x x j h h i j Ru hin to rtin lngth x

Rsults Prolm: HYBRIDIZATION NUMBER Givn: Colltion of phylognti trs T, h on th sm n lvs, k N Qustion: Dos thr xist phylognti ntwork tht isplys h tr in T n hs hyriiztion numr t most k? Two inry trs: Dirt rltionship to mximum yli grmnt forst (MAAF) O((28k)k + n3 )-tim lgorithm (Borwih & Smpl 2007) O(3.8k n)- tim lgorithm (Whin, Biko & Zh, 203) Sm pproximility s irt fk vrtx st (Klk, vi, Lki, Linz, Sornv, Stougi, 202) Any numr of noninry trs: (vi, Klk & Sornv, 204) Krnl with 4k(5k) t lvs, with t th numr of trs Krnl with 20k2 ( + ) lvs, with + th mximum outgr n f (k) t-tim oun-srh lgorithm, with f stronomil Thr inry trs: k poly(n) tim lgorithm (vi, Lki, Klk, Whin & Zh, 204) ( = 60989840)

PART 2: NETWORKS FROM SUBNETWORKS

Enoing Trs Trs r no y thir triplts.

Enoing Trs Trs r no y thir triplts. Trs r no y thir lustrs. {} {} {} {} {, } {, } {,,, } {,,,, }

Enoing Trs Trs r no y thir triplts. Trs r no y thir lustrs. Trs r no y thir istns. 4 2 2 0 2 6 6 8 2 0 6 6 8 6 6 0 2 8 6 6 2 0 8 8 8 8 8 0

Enoing Trs Trs r no y thir triplts. Trs r no y thir lustrs. Trs r no y thir istns. Cn w no ntworks? 4 2 2 0 2 6 6 8 2 0 6 6 8 6 6 0 2 8 6 6 2 0 8 8 8 8 8 0

Enoing Ntworks Trs r no y thir triplts. Ntworks r not no y thir triplts.

Trints n Sunts Trs r no y thir triplts. Ar ntworks no y thir trints?? N T (N )

Trints n Sunts Th sunt N X is otin from N y. lting ll vrtis tht r not on ny pth from th root to lf in X ; 2. lting ll vrtis tht r on ll pths from th root to lf in X ; 3. supprssing ingr- outgr- vrtis n prlll rs.? N T (N )

Trints n Sunts Th sunt N X is otin from N y. lting ll vrtis tht r not on ny pth from th root to lf in X ; 2. lting ll vrtis tht r on ll pths from th root to lf in X ; 3. supprssing ingr- outgr- vrtis n prlll rs.? N T (N )

Trints n Sunts Th sunt N X is otin from N y. lting ll vrtis tht r not on ny pth from th root to lf in X ; 2. lting ll vrtis tht r on ll pths from th root to lf in X ; 3. supprssing ingr- outgr- vrtis n prlll rs.? N T (N )

Trints n Sunts A trint is sunt with 3 lvs. A int is sunt with 2 lvs.? N T (N )

Trints n Sunts Dfinition. lvl-k: h ionnt omponnt hs hyriiztion numr k; tr-hil: h non-lf vrtx hs hil with ingr-.? N T (N )

Trints n Sunts Dfinition. lvl-k: h ionnt omponnt hs hyriiztion numr k; tr-hil: h non-lf vrtx hs hil with ingr-. Thorm. (Hur, vi & Moulton) Binry lvl-, lvl-2 n tr-hil ntworks r ll no y thir trints.? N T (N )

Trints n Sunts Dfinition. lvl-k: h ionnt omponnt hs hyriiztion numr k; tr-hil: h non-lf vrtx hs hil with ingr-. Thorm. (Hur, vi & Moulton) Binry lvl-, lvl-2 n tr-hil ntworks r ll no y thir trints. & Wu, 205) Thorm. (Hur, vi, Moulton y thir sunts. Gnrl (inry) ntworks r not no? N T (N )

Ronstruting trs from triplts Trs r no y thir triplts

Ronstruting trs from triplts Trs r no y thir triplts n givn ny st of triplts, w n onstrut tr isplying thm, if on xists, in polynomil tim. (Aho, Sgiv, Szymnski, Ullmn, 98)

Ronstruting ntworks from trints Lvl- ntworks r no y thir trints n givn omplt st of trints, w n onstrut lvl- ntwork isplying thm, if on xists, in polynomil tim. (Hur & Moulton, 203)

Ronstruting ntworks from trints Lvl- ntworks r no y thir trints n givn omplt st of trints, w n onstrut lvl- ntwork isplying thm, if on xists, in polynomil tim. (Hur & Moulton, 203) for n ritrry st of trints, this is NP-hr ut solvl in O(3n poly(n)) tim (Hur, vi, Moulton, Sornv & Wu 204)

Ronstruting ntworks from trints Lvl- ntworks r no y thir trints n givn omplt st of trints, w n onstrut lvl- ntwork isplying thm, if on xists, in polynomil tim. (Hur & Moulton, 203) for n ritrry st of trints, this is NP-hr ut solvl in O(3n poly(n)) tim for n ritrry st of ints, this is polynomil-tim solvl (Hur, vi, Moulton, Sornv & Wu 204)

Ronstruting ntworks from trints Lvl- ntworks r no y thir trints n givn omplt st of trints, w n onstrut lvl- ntwork isplying thm, if on xists, in polynomil tim. (Hur & Moulton, 203) for n ritrry st of trints, this is NP-hr ut solvl in O(3n poly(n)) tim for n ritrry st of ints, this is polynomil-tim solvl n lso for sunts in whih ll yls hv siz 3. (Hur, vi, Moulton, Sornv & Wu 204)

Suprntwork Mthos g f f g N f g f g f g N N isplys T N isplys N T

PART 3: NETWORKS FROM SEQUENCES

Mximum Prsimony for trs Smll prsimony prolm: givn tr n squn for h lf, ssign squns to th intrnl vrtis in orr to minimiz th totl numr of hngs. ACCTG ATCTG ATCTC GTAAA TTACT Exmpl input Lo vn Irsl (TUD) Introuing nw ollgus 3TU.AMI 8 mr 205 / 2

Mximum Prsimony for trs Smll prsimony prolm: givn tr n squn for h lf, ssign squns to th intrnl vrtis in orr to minimiz th totl numr of hngs. TTCTA ATCTA TTAAA ATCTG ACCTG ATCTG ATCTC GTAAA TTACT Exmpl llling of intrnl vrtis Lo vn Irsl (TUD) Introuing nw ollgus 3TU.AMI 8 mr 205 2 / 2

Mximum Prsimony for trs Smll prsimony prolm: givn tr n squn for h lf, ssign squns to th intrnl vrtis in orr to minimiz th totl numr of hngs. TTCTA ATCTA TTAAA ATCTG ACCTG ATCTG ATCTC GTAAA TTACT Exmpl of on hng Lo vn Irsl (TUD) Introuing nw ollgus 3TU.AMI 8 mr 205 3 / 2

Mximum Prsimony for trs Smll prsimony prolm: givn tr n squn for h lf, ssign squns to th intrnl vrtis in orr to minimiz th totl numr of hngs. TTCTA 2 ATCTA ATCTG TTAAA ACCTG ATCTG ATCTC 2 GTAAA TTACT Th prsimony sor is 9. Lo vn Irsl (TUD) Introuing nw ollgus 3TU.AMI 8 mr 205 4 / 2

Mximum Prsimony for trs Smll prsimony prolm: givn tr n squn for h lf, ssign squns to th intrior vrtis in orr to minimiz th totl numr of hngs. Polynomil-tim solvl: Consir h hrtr (position in th squns) sprtly. Us ynmi progrmming (Fith, 97). Lo vn Irsl (TUD) Introuing nw ollgus 3TU.AMI 8 mr 205 5 / 2

Smll Prsimony Prolm on Ntworks Givn ntwork n stt for h lf. Hrwir Prsimony Sor: th minimum numr of stt-hngs ovr ll possil ssignmnts of stts to intrnl vrtis. Softwir Prsimony Sor: th minimum prsimony sor of tr isply y th ntwork. Lo vn Irsl (TUD) Introuing nw ollgus 3TU.AMI 8 mr 205 6 / 2

Exmpl: Input 2 Lo vn Irsl (TUD) 2 2 Introuing nw ollgus 3TU.AMI 3 8 mr 205 7 / 2

Possil signmnt of stts to intrnl vrtis 2 2 2 2 2 Lo vn Irsl (TUD) 2 2 Introuing nw ollgus 3TU.AMI 3 8 mr 205 8 / 2

Hrwir Prsimony Sor = 4 2 2 2 2 2 Lo vn Irsl (TUD) 2 2 Introuing nw ollgus 3TU.AMI 3 8 mr 205 9 / 2

On of th two trs isply y th ntwork 2 Lo vn Irsl (TUD) 2 2 Introuing nw ollgus 3TU.AMI 3 8 mr 205 0 / 2

Th prsimony sor of this tr is 3 2 2 2 2 2 Lo vn Irsl (TUD) 2 2 Introuing nw ollgus 3TU.AMI 3 8 mr 205 / 2

Th prsimony sor of th othr tr is 4 2 2 2 2 2 2 2 3 Th softwir prsimony sor of th ntwork is min{3, 4} = 3 Lo vn Irsl (TUD) Introuing nw ollgus 3TU.AMI 8 mr 205 2 / 2

Hrwir n Softwir sors n ritrrily fr prt 0 0 0 0 0 0 Lo vn Irsl (TUD) 0 Introuing nw ollgus 3TU.AMI 8 mr 205 3 / 2

Hrwir n Softwir sors n ritrrily fr prt 0 0 0 0 0 0 0 Softwir Prsimony Sor = 2 Lo vn Irsl (TUD) Introuing nw ollgus 3TU.AMI 8 mr 205 4 / 2

Hrwir n Softwir sors n ritrrily fr prt 0 0 0 0 0 0 0 Softwir Prsimony Sor = 2 Hrwir Prsimony Sor = Hyriiztion Numr + Lo vn Irsl (TUD) Introuing nw ollgus 3TU.AMI 8 mr 205 5 / 2

Th hrwir prsimony sor quls th siz of minimum multitrminl ut in th grph otin y mrging ll lvs with th sm stt into singl vrtx, n ltting th mrg vrtis th trminls. 0 0 0 0 0 0 Lo vn Irsl (TUD) 0 Introuing nw ollgus 3TU.AMI 8 mr 205 6 / 2

Th hrwir prsimony sor quls th siz of minimum multitrminl ut in th grph otin y mrging ll lvs with th sm stt into singl vrtx, n ltting th mrg vrtis th trminls. 0 Lo vn Irsl (TUD) Introuing nw ollgus 3TU.AMI 8 mr 205 7 / 2

Th hrwir prsimony sor quls th siz of minimum multitrminl ut in th grph otin y mrging ll lvs with th sm stt into singl vrtx, n ltting th mrg vrtis th trminls. 0 Lo vn Irsl (TUD) Introuing nw ollgus 3TU.AMI 8 mr 205 8 / 2

Th hrwir prsimony sor n omput in polynomil tim whn thr r two stts, Lo vn Irsl (TUD) Introuing nw ollgus 3TU.AMI 8 mr 205 9 / 2

Th hrwir prsimony sor n omput in polynomil tim whn thr r two stts, n pproximt wll whn thr r mor thn two stts. Lo vn Irsl (TUD) Introuing nw ollgus 3TU.AMI 8 mr 205 9 / 2

Th hrwir prsimony sor n omput in polynomil tim whn thr r two stts, n pproximt wll whn thr r mor thn two stts. Thorm (Fishr, vi, Klk & Sornv, 205) For vry onstnt ǫ > 0 thr is no polynomil-tim pproximtion lgorithm tht pproximts th softwir prsimony sor to ftor n ǫ for ntwork n inry hrtr, unlss P = NP. Lo vn Irsl (TUD) Introuing nw ollgus 3TU.AMI 8 mr 205 9 / 2

Th hrwir prsimony sor n omput in polynomil tim whn thr r two stts, n pproximt wll whn thr r mor thn two stts. Thorm (Fishr, vi, Klk & Sornv, 205) For vry onstnt ǫ > 0 thr is no polynomil-tim pproximtion lgorithm tht pproximts th softwir prsimony sor to ftor n ǫ for ntwork n inry hrtr, unlss P = NP. Lukily, th softwir prsimony sor n omput ffiintly whn th hyriiztion numr (or lvl ) of th ntwork is smll. Lo vn Irsl (TUD) Introuing nw ollgus 3TU.AMI 8 mr 205 9 / 2

Min opn qustions (from ll prts) Is thr is n FPT lgorithm for Hyriiztion Numr on multipl noninry trs n th hyriiztion numr s only prmtr. Lo vn Irsl (TUD) Introuing nw ollgus 3TU.AMI 8 mr 205 20 / 2

Min opn qustions (from ll prts) Is thr is n FPT lgorithm for Hyriiztion Numr on multipl noninry trs n th hyriiztion numr s only prmtr. Whih lsss of ntworks r no y trints? Lo vn Irsl (TUD) Introuing nw ollgus 3TU.AMI 8 mr 205 20 / 2

Min opn qustions (from ll prts) Is thr is n FPT lgorithm for Hyriiztion Numr on multipl noninry trs n th hyriiztion numr s only prmtr. Whih lsss of ntworks r no y trints? How n w srh for ntwork with optiml softwir prsimony sor, ovr ll ntworks with hyriiztion numr t most k? Lo vn Irsl (TUD) Introuing nw ollgus 3TU.AMI 8 mr 205 20 / 2

Thnks Mrik Fishr (Grifswl) Kthrin Hur (Norwih) Stvn Klk (Mstriht) Nl Lki (Mstriht) Simon Linz (Christhurh) Vinnt Moulton (Norwih) Clin Sornv (Montpllir) Ln Stougi (Amstrm) Toyng Wu (Norwih) Lo vn Irsl (TUD) Introuing nw ollgus 3TU.AMI 8 mr 205 2 / 2

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