adjustment to convergegross substitutesDressWenzel 91 generalize G - PDF document

1 adjustment to converg
adjustment to converg

2 egross substitutes[Dr
egross substitutes[Dr

3 ess-Wenzel Õ91] gener
ess-Wenzel Õ91] gener

4 alize Grassmann-Pluck
alize Grassmann-Pluck

5 er relationsvaluated
er relationsvaluated

6 matroids matroidal ma
matroids matroidal ma

7 ps[Murota-Shioura Õ99
ps[Murota-Shioura Õ99

8 ] generalize convexit
] generalize convexit

9 y to discrete domains
y to discrete domains

10 adjustment to conver
adjustment to conver

11 gegross substitutes[D
gegross substitutes[D

12 ress-Wenzel Õ91] gene
ress-Wenzel Õ91] gene

13 ralize Grassmann-Pluc
ralize Grassmann-Pluc

14 ker relationsvaluated
ker relationsvaluated

15 matroids matroidal m
matroids matroidal m

16 aps[Murota-Shioura Õ9
aps[Murota-Shioura Õ9

17 9] generalize convexi
9] generalize convexi

18 ty to discrete domain
ty to discrete domain

19 s ¥Some examples of G
s ¥Some examples of G

20 S: ¥additive function
S: ¥additive function

21 s ¥unit-demand ¥match
s ¥unit-demand ¥match

22 ing valuations
ing valuations

23 max matching from
max matching from

24 S v(S)=!i!Sv(i)v(S)=
S v(S)=!i!Sv(i)v(S)=

25 maxi!Sv(i)v(S)= ¥Some
maxi!Sv(i)v(S)= ¥Some

26 examples of GS: ¥add
examples of GS: ¥add

27 itive functions ¥unit
itive functions ¥unit

28 -demand ¥matching val
-demand ¥matching val

29 uations max
uations max

30 matching from S v(S)
matching from S v(S)

31 =!i!Sv(i)v(S)=maxi!Sv
=!i!Sv(i)v(S)=maxi!Sv

32 (i)v(S)= ¥Some exampl
(i)v(S)= ¥Some exampl

33 es of GS: ¥additive f
es of GS: ¥additive f

34 unctions ¥unit-demand
unctions ¥unit-demand

35 ¥matching valuations
¥matching valuations

36 max matchi
max matchi

37 ng from S v(S)=!i!Sv(
ng from S v(S)=!i!Sv(

38 i)v(S)=maxi!Sv(i)v(S)
i)v(S)=maxi!Sv(i)v(S)

39 = ¥Some examples of G
= ¥Some examples of G

40 S: ¥additive function
S: ¥additive function

41 s ¥unit-demand ¥match
s ¥unit-demand ¥match

42 ing valuations
ing valuations

43 max matching from
max matching from

44 S v(S)=!i!Sv(i)v(S)=
S v(S)=!i!Sv(i)v(S)=

45 maxi!Sv(i)v(S)= ¥Some
maxi!Sv(i)v(S)= ¥Some

46 examples of GS: ¥add
examples of GS: ¥add

47 itive functions ¥unit
itive functions ¥unit

48 -demand ¥matching val
-demand ¥matching val

49 uations max
uations max

50 matching from S v(S)
matching from S v(S)

51 =!i!Sv(i)v(S)=maxi!Sv
=!i!Sv(i)v(S)=maxi!Sv

52 (i)v(S)= ¥Some exampl
(i)v(S)= ¥Some exampl

53 es of GS: ¥additive f
es of GS: ¥additive f

54 unctions ¥unit-demand
unctions ¥unit-demand

55 ¥matching valuations
¥matching valuations

56 max matchi
max matchi

57 ng from S ¥matroid-ma
ng from S ¥matroid-ma

58 tchingv(S)=!i!Sv(i)v(
tchingv(S)=!i!Sv(i)v(

59 S)=maxi!Sv(i)v(S)= ¥S
S)=maxi!Sv(i)v(S)= ¥S

60 ome examples of GS: ¥
ome examples of GS: ¥

61 additive functions ¥u
additive functions ¥u

62 nit-demand ¥matching
nit-demand ¥matching

63 valuations
valuations

64 max matching from S ¥
max matching from S ¥

65 matroid-matchingv(S)=
matroid-matchingv(S)=

66 !i!Sv(i)v(S)=maxi!Sv(
!i!Sv(i)v(S)=maxi!Sv(

67 i)v(S)= ¥Some example
i)v(S)= ¥Some example

68 s of GS: ¥additive fu
s of GS: ¥additive fu

69 nctions ¥unit-demand
nctions ¥unit-demand

70 ¥matching valuations
¥matching valuations

71 max matchin
max matchin

72 g from S ¥matroid-mat
g from S ¥matroid-mat

73 chingv(S)=!i!Sv(i)v(S
chingv(S)=!i!Sv(i)v(S

74 )=maxi!Sv(i)v(S)= adj
)=maxi!Sv(i)v(S)= adj

75 ustment to convergegr
ustment to convergegr

76 oss substitutes[Dress
oss substitutes[Dress

77 -Wenzel Õ91] generali
-Wenzel Õ91] generali

78 ze Grassmann-Plucker
ze Grassmann-Plucker

79 relationsvaluated mat
relationsvaluated mat

80 roids matroidal maps[
roids matroidal maps[

81 Murota-Shioura Õ99] g
Murota-Shioura Õ99] g

82 eneralize convexity t
eneralize convexity t

83 o discrete domains ad
o discrete domains ad

84 justment to convergeg
justment to convergeg

85 ross substitutes[Dres
ross substitutes[Dres

86 s-Wenzel Õ91] general
s-Wenzel Õ91] general

87 ize Grassmann-Plucker
ize Grassmann-Plucker

88 relationsvaluated ma
relationsvaluated ma

89 troids matroidal maps
troids matroidal maps

90 [Murota-Shioura Õ99]
[Murota-Shioura Õ99]

91 generalize convexity
generalize convexity

92 to discrete domains a
to discrete domains a

93 djustment to converge
djustment to converge

94 gross substitutes[Dre
gross substitutes[Dre

95 ss-Wenzel Õ91] genera
ss-Wenzel Õ91] genera

96 lize Grassmann-Plucke
lize Grassmann-Plucke

97 r relationsvaluated m
r relationsvaluated m

98 atroids matroidal map
atroids matroidal map

99 s[Murota-Shioura Õ99]
s[Murota-Shioura Õ99]

100 generalize convexity
generalize convexity

101 to discrete domains
to discrete domains

102 demand oracle problem
demand oracle problem

103 !j"(p)=1 sgn ÷v(S)=v
!j"(p)=1 sgn ÷v(S)=v

104 (S)+p0!!i!Spiv1!v2(S)
(S)+p0!!i!Spiv1!v2(S)

105 =maxT!Sv1(T)+v2(S\T)÷
=maxT!Sv1(T)+v2(S\T)÷

106 v(S)= ÷v(S)=v(S)+p0!!
v(S)= ÷v(S)=v(S)+p0!!

107 i!Spiv1!v2(S)=maxT!Sv
i!Spiv1!v2(S)=maxT!Sv