adjustment to convergegross substitutesDressWenzel ID: 845617
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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