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[][]\T1/LinuxLibertineT-TLF/m/sc/9 (-20) Problem 1.1. []\T1/LinuxLibertineT-TLF
/m/it/9 (-20) Given a $\OML/nxlmi/m/it/9 c$\T1/LinuxLibertineT-TLF/m/n/9 (-20)
-TIDB $\LMS/ntxsy/m/n/9 D \U/ntxmia/m/it/9 = []$\T1/LinuxLibertineT-TLF/m/it/9
(-20) , $[][]$ query[][][]
[]
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\OML/nxlmi/m/it/9 Q$\T1/LinuxLibertineT-TLF/m/it/9 (-20) , and re-sult tu-ple $
\OML/nxlmi/m/it/9 t$\T1/LinuxLibertineT-TLF/m/it/9 (-20) , com-pute the ex-pect
ed mul-ti-plic-ity of $\OML/nxlmi/m/it/9 t$\T1/LinuxLibertineT-TLF/m/it/9 (-20)
: $[][] []$.
[]
[1.1{c:/texlive/2020/texmf-var/fonts/map/pdftex/updmap/pdftex.map}
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[][]
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\T1/LinuxLibertineT-TLF/m/n/9 (-20) go-rithm that com-putes Prob-lem []1.1[] in
time $\OML/nxlmi/m/it/9 O[] []$\T1/LinuxLibertineT-TLF/m/n/9 (-20) .
[]
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\T1/LinuxLibertineT-TLF/m/n/9 (-20) This means, when we are okay with ap-prox-i
-ma-tion, that we solve Prob-
[]
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\T1/LinuxLibertineT-TLF/m/n/9 (-20) tech-niques ([[], []]) in set-PDBs need tim
e $\U/ntxmia/m/it/9
\LMS/ntxsy/m/n/9 <20>\OML/nxlmi/m/it/9 T[] [][]\LMS/ntxsy/m/n/9 <20>$
[]
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[]
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\T1/LinuxLibertineT-TLF/m/it/9 (-20) the ex-pected mul-ti-plic-ity of the poly-
no-mial $\U/ntxmia/m/it/9 ^^H\LMS/ntxsy/m/n/9 <20>\OML/nxlmi/m/it/9 Q; D; t\LMS/nt
xsy/m/n/9 <20>$ \T1/LinuxLibertineT-TLF/m/it/9 (-20) (i.e., $[][] []$,
[]
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\OML/nxlmi/m/it/9 Q[] \LMS/ntxsy/m/n/9 ^^B \OML/nxlmi/m/it/9 Q[]$\T1/LinuxLiber
tineT-TLF/m/n/9 (-20) . The lin-eage poly-no-mial for $\OML/nxlmi/m/it/9 Q[]$ \
T1/LinuxLibertineT-TLF/m/n/9 (-20) is given by $\U/ntxmia/m/it/9 ^^H[] []$
[]
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[]$[] \U/ntxmia/m/it/9 ^^H[] [] = ^^H[] []$
[]
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\T1/LinuxLibertineT-TLF/m/n/9 (-20) Com-put-ing ex-pec-ta-tion we get $[] [] \U
/ntxmia/m/it/9 = [][] \OML/nxlmi/m/it/9 j[]j[]j[] [] [] [] [] [] []$\T1/LinuxLi
bertineT-TLF/m/n/9 (-20) ,
[]
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[]$[]\OML/nxlmi/m/it/9 A [] B \LMS/ntxsy/m/n/9 <20> \OML/nxlmi/m/it/9 BYE \LMS/nt
xsy/m/n/9 <20> \OML/nxlmi/m/it/9 BZC \LMS/ntxsy/m/n/9 <20> \OT1/LinuxLibertineT-TLF/m
/n/9 2\OML/nxlmi/m/it/9 A [] BYE \LMS/ntxsy/m/n/9 <20> \OT1/LinuxLibertineT-TLF/m/
n/9 2\OML/nxlmi/m/it/9 A [] BZC \LMS/ntxsy/m/n/9 <20> \OT1/LinuxLibertineT-TLF/m/n
/9 2\OML/nxlmi/m/it/9 BYEZC \U/ntxmia/m/it/9 =$
[]
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[]$[]\OML/nxlmi/m/it/9 ABX[] \LMS/ntxsy/m/n/9 <20> \OML/nxlmi/m/it/9 AB [][] X[]
\LMS/ntxsy/m/n/9 <20> \OML/nxlmi/m/it/9 BYE \LMS/ntxsy/m/n/9 <20> \OML/nxlmi/m/it/9 B
ZC \LMS/ntxsy/m/n/9 <20> \OT1/LinuxLibertineT-TLF/m/n/9 2\OML/nxlmi/m/it/9 AX[]BYE
\LMS/ntxsy/m/n/9 <20> \OT1/LinuxLibertineT-TLF/m/n/9 2\OML/nxlmi/m/it/9 A [][] X[
]BYE \LMS/ntxsy/m/n/9 <20> \OT1/LinuxLibertineT-TLF/m/n/9 2\OML/nxlmi/m/it/9 AX[]B
ZC \LMS/ntxsy/m/n/9 <20> \OT1/LinuxLibertineT-TLF/m/n/9 2\OML/nxlmi/m/it/9 A [][]
X[]BZC \LMS/ntxsy/m/n/9 <20> \OT1/LinuxLibertineT-TLF/m/n/9 2\OML/nxlmi/m/it/9 BYE
ZC: $
[]
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\T1/LinuxLibertineT-TLF/m/n/9 (-20) tion that we want is $[]\LMS/ntxsy/m/n/9 <20>\
OML/nxlmi/m/it/9 Pr [] ;$ $Pr [] ; Pr []\LMS/ntxsy/m/n/9 <20>\OML/nxlmi/m/it/9 ; P
r [] ; Pr [] ; Pr [] ; Pr [] ; Pr []\LMS/ntxsy/m/n/9 <20>$\T1/LinuxLibertineT-TLF/
m/n/9 (-20) .
[]
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\pgfarrowinset=\dimen349
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[][]
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\T1/LinuxLibertineT-TLF/m/n/9 (-20) TIDB $\LMS/ntxsy/m/n/9 D$\T1/LinuxLibertine
T-TLF/m/it/9 (-20) , $[][]$ query $\OML/nxlmi/m/it/9 Q$\T1/LinuxLibertineT-TLF/
m/it/9 (-20) , is there a $\LMS/ntxsy/m/n/9 <20>\OT1/LinuxLibertineT-TLF/m/n/9 (-2
0) 1 \LMS/ntxsy/m/n/9 ^^F \OML/nxlmi/m/it/9 ^^O\LMS/ntxsy/m/n/9 <20>$\T1/LinuxLibe
rtineT-TLF/m/it/9 (-20) -approximation of $[][] []$
[]
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\T1/LinuxLibertineT-TLF/m/it/9 (-20) for all re-sult tu-ples $\OML/nxlmi/m/it/9
t$ \T1/LinuxLibertineT-TLF/m/it/9 (-20) where $\LMS/ntxsy/m/n/9 9[] \OT1/Linux
LibertineT-TLF/m/n/9 (-20) : \OML/nxlmi/m/it/9 T[]\LMS/ntxsy/m/n/9 <20>\OML/nxlmi/
m/it/9 Q; D; []\LMS/ntxsy/m/n/9 <20> <20> \OML/nxlmi/m/it/9 T[]\LMS/ntxsy/m/n/9 <20>[]\O
ML/nxlmi/m/it/9 ; ^^O\LMS/ntxsy/m/n/9 <20> ^^T \OML/nxlmi/m/it/9 O[]\LMS/ntxsy/m/n
/9 <20>\OML/nxlmi/m/it/9 T[] []\LMS/ntxsy/m/n/9 <20>$\T1/LinuxLibertineT-TLF/m/it/9 (
-20) ?
[]
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[]\T1/LinuxLibertineT-TLF/m/n/9 (-20) Given that there ex-ists a rep-re-sen-ta-
tion $[][]$ such that $\OML/nxlmi/m/it/9 T[]\LMS/ntxsy/m/n/9 <20>\OML/nxlmi/m/it/9
Q; D; [][]\LMS/ntxsy/m/n/9 <20> ^^T
[]
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\T1/LinuxLibertineT-TLF/m/n/9 (-20) the ques-tion of ap-prox-i-ma-tion can be s
tated as the fol-low-ing stronger
[]
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\T1/LinuxLibertineT-TLF/m/n/9 (-20) (since Prob-lem []1.5[] has ac-cess to \T1/
LinuxLibertineT-TLF/m/it/9 (-20) all \T1/LinuxLibertineT-TLF/m/n/9 (-20) equiv-
a-lent \T1/zi4/m/it/9 C \T1/LinuxLibertineT-TLF/m/n/9 (-20) rep-re-sent-ing $\O
ML/nxlmi/m/it/9 Q [] []$\T1/LinuxLibertineT-TLF/m/n/9 (-20) ),
[]
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[][]\T1/LinuxLibertineT-TLF/m/sc/9 (-20) Definition 2.1 (Stan-dard Mono-mial Ba
-sis). []\T1/LinuxLibertineT-TLF/m/it/9 (-20) The term $[][] \OML/nxlmi/m/it/9
X[]$
[]
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[][]\T1/LinuxLibertineT-TLF/m/sc/9 (-20) Proposition 2.4 ($\OML/nxlmi/m/it/9 c$
\T1/LinuxLibertineT-TLF/m/n/9 (-20) -TIDB \T1/LinuxLibertineT-TLF/m/sc/9 (-20)
re-duc-tion). []\T1/LinuxLibertineT-TLF/m/it/9 (-20) Given $\OML/nxlmi/m/it/9 c
$\T1/LinuxLibertineT-TLF/m/n/9 (-20) -TIDB $\LMS/ntxsy/m/n/9 D \U/ntxmia/m/it/9
= []$\T1/LinuxLibertineT-TLF/m/it/9 (-20) ,
[]
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\T1/LinuxLibertineT-TLF/m/it/9 (-20) eage poly-no-mial $\U/ntxmia/m/it/9 ^^H[]
[] = ^^H[] [] []$\T1/LinuxLibertineT-TLF/m/it/9 (-20) , it holds that $[][] []
\U/ntxmia/m/it/9 =
[]
) (./pwsem.tex
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[]$\T1/LinuxLibertineT-TLF/m/n/9 (-20) , show-ing Prob-lem []1.2[] can-not be d
one in $\OML/nxlmi/m/it/9 O []$
[]
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[][]\T1/LinuxLibertineT-TLF/m/sc/9 (-20) Lemma 3.5. []\T1/LinuxLibertineT-TLF/m
/it/9 (-20) Let $\OML/nxlmi/m/it/9 Q[]$ \T1/LinuxLibertineT-TLF/m/it/9 (-20) an
d $\OML/nxlmi/m/it/9 D$ \T1/LinuxLibertineT-TLF/m/it/9 (-20) be as de-fined abo
ve. Then $\OML/nxlmi/m/it/9 T[] []$
[]
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[7.7]) (./single_p.tex
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\T1/LinuxLibertineT-TLF/m/n/9 (-20) In Sec. []3[], we showed that Prob-lem []1.
2[] can-not be solved in $\OML/nxlmi/m/it/9 O []$
[]
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[]$
[]
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[8.8]
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[][]\OML/nxlmi/m/it/9 O [] :
[]
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\T1/LinuxLibertineT-TLF/m/it/9 (-20) run-time sim-pli-fies to $\OML/nxlmi/m/it/
9 O[] []$\T1/LinuxLibertineT-TLF/m/it/9 (-20) .
[]
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[]\T1/LinuxLibertineT-TLF/m/n/9 (-20) Finally, we ad-dress the $[] []$ term
[]
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\T1/LinuxLibertineT-TLF/m/n/9 (-20) If $[]$ is a tree, then the run-time sim-pl
i-fies to $\OML/nxlmi/m/it/9 O[] []$\T1/LinuxLibertineT-TLF/m/n/9 (-20) ,
[]
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[][]\T1/LinuxLibertineT-TLF/m/sc/9 (-20) Corollary 4.10. []\T1/LinuxLibertineT-
TLF/m/it/9 (-20) Let $\OML/nxlmi/m/it/9 Q$ \T1/LinuxLibertineT-TLF/m/it/9 (-20)
be an $[][]$ query and $\LMS/ntxsy/m/n/9 D$ \T1/LinuxLibertineT-TLF/m/it/9 (-2
0) be a []
[]
) (./related-work.tex [9.9]) (./conclusions.tex) Processing 'acks' comment.
\openout3 = `comment.cut'.
Comment 'acks' writing to comment.cut. Straight input of comment.cut.
(./comment.cut (./acknowledgements.tex)) (./main.bbl
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[10.10])
[11.11
] (./appendix.tex (./app_set-to-bag-pdb.tex)
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\OML/nxlmi/m/it/9 Q\LMS/ntxsy/m/n/9 <20>\OML/nxlmi/m/it/9 D[]\LMS/ntxsy/m/n/9 <20><>\O
ML/nxlmi/m/it/9 t\LMS/ntxsy/m/n/9 <20>$\T1/LinuxLibertineT-TLF/m/n/9 (-20) , and a
s be-fore, in-ter-pret it as a func-tion $\U/ntxmia/m/it/9 ^^H\LMS/ntxsy/m/n/9
<EFBFBD>\OML/nxlmi/m/it/9 Q; D[]; t\LMS/ntxsy/m/n/9 <20> \OT1/LinuxLibertineT-TLF/m/n/9 (
-20) :
[]
) (./app_notation-background.tex [12.12
]
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[]\T1/LinuxLibertineT-TLF/m/n/9 (-20) Since $\U/ntxsym/m/n/9 N\LMS/ntxsy/m/n/9
<EFBFBD>\OT1/LinuxLibertineT-TLF/sb/n/9 (-20) X\LMS/ntxsy/m/n/9 <20>$ \T1/LinuxLibertineT
-TLF/m/n/9 (-20) is the free ob-ject in the va-ri-ety of semir-ings, Birkhoff's
[]
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[]
[]
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\T1/LinuxLibertineT-TLF/m/n/9 (-20) The in-ner sum is only over $\OT1/LinuxLibe
rtineT-TLF/sb/n/9 (-20) w$ \T1/LinuxLibertineT-TLF/m/n/9 (-20) where $\OML/nxlm
i/m/it/9 []\LMS/ntxsy/m/n/9 <20>D[]<5D> \U/ntxmia/m/it/9 = \OML/nxlmi/m/it/9 D$ \T1/
LinuxLibertineT-TLF/m/n/9 (-20) (i.e., $\OML/nxlmi/m/it/9 Q\LMS/ntxsy/m/n/9 <20>\O
ML/nxlmi/m/it/9 D[]\LMS/ntxsy/m/n/9 <20><>\OML/nxlmi/m/it/9 t\LMS/ntxsy/m/n/9 <20><>\OT
1/LinuxLibertineT-TLF/sb/n/9 (-20) w\LMS/ntxsy/m/n/9 <20> \U/ntxmia/m/it/9 =
[]
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\T1/LinuxLibertineT-TLF/m/n/9 (-20) The in-ner sum is only over $\OT1/LinuxLibe
rtineT-TLF/sb/n/9 (-20) w$ \T1/LinuxLibertineT-TLF/m/n/9 (-20) where $\OML/nxlm
i/m/it/9 []\LMS/ntxsy/m/n/9 <20>D[]<5D> \U/ntxmia/m/it/9 = \OML/nxlmi/m/it/9 D$ \T1/
LinuxLibertineT-TLF/m/n/9 (-20) (i.e., $\OML/nxlmi/m/it/9 Q\LMS/ntxsy/m/n/9 <20>\O
ML/nxlmi/m/it/9 D[]\LMS/ntxsy/m/n/9 <20><>\OML/nxlmi/m/it/9 t\LMS/ntxsy/m/n/9 <20><>\OT
1/LinuxLibertineT-TLF/sb/n/9 (-20) w\LMS/ntxsy/m/n/9 <20> \U/ntxmia/m/it/9 =
[]
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[]
[]
[13.13]
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[][]\T1/LinuxLibertineT-TLF/m/sc/9 (-20) Proposition B.4. []\T1/LinuxLibertineT
-TLF/m/it/9 (-20) For any BIDB-lineage poly-no-mial $\U/ntxmia/m/it/9 ^^H\LMS/n
txsy/m/n/9 <20>\OML/nxlmi/m/it/9 X[]; [] ; X[]\LMS/ntxsy/m/n/9 <20>$
[]
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[]
[]
) (./app_hardness-results.tex
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[14.14]
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[]
[]
[16.16])
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[]\T1/LinuxLibertineT-TLF/m/n/9 (-20) Since these two se-lec-tions can be made
in-de-pen-dently, $[] \U/ntxmia/m/it/9 =
[]
[17.17]
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[]$\T1/LinuxLibertineT-TLF/m/n/9 (-20) , $[]$, $[] \OML/nxlmi/m/it/9 ;$
[]
(./app_hard_linsys.tex
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[]
[]
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[]
[]
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[]
[]
[18.18]
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) (./app_approx-alg-analysis.tex
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\U/ntxmia/m/it/9 ^^H\LMS/ntxsy/m/n/9 <20>\OT1/LinuxLibertineT-TLF/sb/n/9 (-20) X\L
MS/ntxsy/m/n/9 <20> \U/ntxmia/m/it/9 = []\LMS/ntxsy/m/n/9 <20>[]<5D>$ \T1/LinuxLibertine
T-TLF/m/it/9 (-20) and let $\OML/nxlmi/m/it/9 k \U/ntxmia/m/it/9 = []\LMS/ntxsy
/m/n/9 <20>[]<5D>$\T1/LinuxLibertineT-TLF/m/it/9 (-20) . Then an es-ti-mate $\LMS/ntx
sy/m/n/9 E$ \T1/LinuxLibertineT-TLF/m/it/9 (-20) of $[]\LMS/ntxsy/m/n/9 <20>\OML/n
xlmi/m/it/9 p[]; [] ; p[]\LMS/ntxsy/m/n/9 <20>$
[]
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\OML/nxlmi/m/it/8 O []
[]
(./app_approx_alg-pseudo-code.tex
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) [19.19]
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\T1/LinuxLibertineT-TLF/m/it/9 (-20) in $\OML/nxlmi/m/it/9 O []$
[]
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[]\T1/LinuxLibertineT-TLF/m/n/9 (-20) Set $\LMS/ntxsy/m/n/9 E \U/ntxmia/m/it/9
= []\LMS/ntxsy/m/n/9 <20>[]\OML/nxlmi/m/it/9 ; \LMS/ntxsy/m/n/9 <20>\OML/nxlmi/m/it/9
p[]; [] ; p[]\LMS/ntxsy/m/n/9 <20>\OML/nxlmi/m/it/9 ;$
[]
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[]\T1/LinuxLibertineT-TLF/m/n/9 (-20) For the claimed prob-a-bil-ity bound of $
\OML/nxlmi/m/it/9 Pr [] \LMS/ntxsy/m/n/9 ^^T
[]
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\T1/LinuxLibertineT-TLF/m/n/9 (-20) first by Line []3[] (which by Lemma []D.6[]
takes time $\OML/nxlmi/m/it/9 O []$\T1/LinuxLibertineT-TLF/m/n/9 (-20) )
[]
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\T1/LinuxLibertineT-TLF/m/n/9 (-20) by Lemma []D.7[] takes $\OML/nxlmi/m/it/9 O
[]$
[]
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[20.20]
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\T1/LinuxLibertineT-TLF/m/n/9 (-20) ables. Then \T1/zi4/m/sc/9 v \T1/LinuxLiber
tineT-TLF/m/n/9 (-20) yields the set of mono-mi-als $[][] [] \U/ntxmia/m/it/9 =
[][]$
[]
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\T1/LinuxLibertineT-TLF/m/n/9 (-20) since for each el-e-ment in the set of cros
s prod-ucts $[]$
[]
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[]\T1/LinuxLibertineT-TLF/m/n/9 (-20) For no-ta-tional sim-plic-ity de-fine $\O
ML/nxlmi/m/it/9 N \U/ntxmia/m/it/9 = []\LMS/ntxsy/m/n/9 <20>[]<5D>$
[]
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[]\T1/LinuxLibertineT-TLF/m/n/9 (-20) For the in-duc-tive step we con-sider a c
ir-cuit \T1/zi4/m/sc/9 C \T1/LinuxLibertineT-TLF/m/n/9 (-20) such that $[]\LMS/
ntxsy/m/n/9 <20>[]<5D> \U/ntxmia/m/it/9 =
[]
[21.21]) (./app_onepass-analysis.tex
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l.59 \For
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l.66 \Else
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l.70 \EndIf
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l.71 \State
\vari{sum} $\gets \gate.\prt$
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[]\T1/LinuxLibertineT-TLF/m/n/9 (-20) When $[][]\OML/nxlmi/m/it/9 :[] \U/ntxmia
/m/it/9 = \LMS/ntxsy/m/n/9 <20>$\T1/LinuxLibertineT-TLF/m/n/9 (-20) , then by line
[]9[] $[][]$.\T1/zi4/m/sc/9 partial $\U/ntxmia/m/it/9 = [][]$\T1/LinuxLibertin
eT-TLF/m/n/9 (-20) .\T1/zi4/m/sc/9 partial
[]
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\OML/nxlmi/m/it/9 O []$ \T1/LinuxLibertineT-TLF/m/n/9 (-20) time. This can be s
een since
[]
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[] \LMS/ntxsy/m/n/9 <20>\OT1/LinuxLibertineT-TLF/m/n/9 (-20) 1\OML/nxlmi/m/it/9 ;
[] ; \OT1/LinuxLibertineT-TLF/m/n/9 (-20) 1\LMS/ntxsy/m/n/9 <20>$\T1/LinuxLibertin
eT-TLF/m/n/9 (-20) . Hence, by def-i-ni-tion each such op-er-a-tion takes $[] [
]$
[]
) (./app_samp-monom-analysis.tex (./app_samp-monom_pseudo-code.texpdfTeX warnin
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l.13 \State
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[]\T1/LinuxLibertineT-TLF/m/n/9 (-20) We now bound the num-ber of re-cur-sive c
alls in $[]$
[]
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[][]\OT1/LinuxLibertineT-TLF/m/n/9 2[]\LMS/ntxsy/m/n/9 <20>[][]<5D> ^^A [][] <20> \OT1/L
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<EFBFBD> \OT1/LinuxLibertineT-TLF/m/n/9 4 \LMS/ntxsy/m/n/9 <20> \OT1/LinuxLibertineT-TLF/
m/n/9 1
[]
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) (./experiments.tex
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\LMS/ntxsy/m/n/9 D[]$ \T1/LinuxLibertineT-TLF/m/n/9 (-20) is a di-rected acycli
c graph $[]$
[]
[25.25]
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\T1/LinuxLibertineT-TLF/m/n/9 (-20) fol-lows. In each case, let $[]$
[]
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[26.26]
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[]\T1/LinuxLibertineT-TLF/m/n/9 (-20) We prove by in-duc-tion that $[] \LMS/ntx
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[]
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\T1/LinuxLibertineT-TLF/b/n/9 (-20) Selection\T1/LinuxLibertineT-TLF/m/n/9 (-20
) . As-sume that $\OML/nxlmi/m/it/9 Q \U/ntxmia/m/it/9 = \OML/nxlmi/m/it/9 ^^[[
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/ntxmia/m/it/9 =
[]
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\LMS/ntxsy/m/n/9 j\OML/nxlmi/m/it/9 V[]\LMS/ntxsy/m/n/9 j$ \T1/LinuxLibertineT-
TLF/m/n/9 (-20) ver-tices, so from the in-duc-tive as-sump-tion and $\OML/nxlmi
/m/it/9 T[] [] \U/ntxmia/m/it/9 =
[]
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[]
[]
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\T1/LinuxLibertineT-TLF/m/it/9 (-20) base $\OML/nxlmi/m/it/9 D[]$ \T1/LinuxLibe
rtineT-TLF/m/it/9 (-20) and the $[][]$ out-put by Al-go-rithm []4[], the run-ti
me $\OML/nxlmi/m/it/9 T[]\LMS/ntxsy/m/n/9 <20>\OML/nxlmi/m/it/9 Q; D[]; [][]\LMS/n
txsy/m/n/9 <20> ^^T
[]
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[]\T1/LinuxLibertineT-TLF/m/n/9 (-20) By anal-y-sis of Al-go-rithm []4[], in-vo
ked as $[][] \LMS/ntxsy/m/n/9 \OML/nxlmi/m/it/9 LC\LMS/ntxsy/m/n/9 <20>\OML/nxlm
i/m/it/9 Q; D[]; \LMS/ntxsy/m/n/9 f\OML/nxlmi/m/it/9 v[]\LMS/ntxsy/m/n/9 g\OML/
nxlmi/m/it/9 ; \LMS/ntxsy/m/n/9 ;\OML/nxlmi/m/it/9 ; \LMS/ntxsy/m/n/9 f<>\OML/nx
lmi/m/it/9 v[]; \OT1/LinuxLibertineT-TLF/m/n/9 (-20) 0\LMS/ntxsy/m/n/9 <20>g<EFBFBD>$\T1/
LinuxLibertineT-TLF/m/n/9 (-20) .
[]
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[]\T1/LinuxLibertineT-TLF/m/n/9 (-20) Before prov-ing our run-time bound, we fi
rst ob-serve that $\OML/nxlmi/m/it/9 T[] [] \LMS/ntxsy/m/n/9 ^^U
[]
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\T1/LinuxLibertineT-TLF/m/n/9 (-20) (ii) $\OML/nxlmi/m/it/9 O\LMS/ntxsy/m/n/9 <20>
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\OML/nxlmi/m/it/9 .[]/ [] .[]/ Q[]\LMS/ntxsy/m/n/9 <20>\OML/nxlmi/m/it/9 D[]\LMS/
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LMS/ntxsy/m/n/9 <20>[]<5D>\OML/nxlmi/m/it/9 ^^^[]\LMS/ntxsy/m/n/9 <20>\OML/nxlmi/m/it/9
; [] ; []\LMS/ntxsy/m/n/9 <20>\OML/nxlmi/m/it/9 ^^^[]\LMS/ntxsy/m/n/9 <20><><EFBFBD>$
[]
[27.27]) (./related-work-extra.tex)
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