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SEO Keyword summary for en.wikipedia.org/wiki/method_of_equal_shares
Keywords are extracted from the main content of your website and are the primary indicator of the words this page could rank for. By frequenty count we expect your focus keyword to be displaystyle
Focus keyword
Short and long tail
Short Tail Keywords displaystyle cost project |
long Tail Keywords (2 words) equal shares pdisplaystyle p equally among selected project approval voting |
long Tail Keywords (3 words) method of equal among the voters then the cost move to sidebar ddisplaystyle mathrm d project pdisplaystyle p hdisplaystyle mathrm h |
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method equal shares wikipedia
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wikipedia free encyclopedia ballot box icon there are projects example third group voters voted total budget divided equally among voter given click arrow above image order see next steps method project obtained most votes cost its supporters would pay minimises maximal payment selected analogously previous step round supporter needs minimal possible point first run out money fourth some not have enough participate purchase all left candidate equals last now only has afford displaystyle mathrm approx ldots pin iin uip bibn rho geq beginalignedsum nmin leftbiuipcdot rightmathrm ptextendaligned textstyle sum ncolon bimathrm ptext ptextstyle nuip bimax biuipcdot available assign value proportionally values assigned case means from second such pays those get utility thus paymentperutility uniqpostmath qinu different was higher consider payments presented picture equal but still proportional across consequently after every part price except who had any also need nevertheless hence elected note too little paying utilities yet paid circa sixth much fifth rule spent positive savings can afforded algorithm stops outcome further completed according utilitarian strategy per fit within constraint cdot uipmathrm uipuipto infty succ ysucc ixsucc pos delta ipleq bigeq nbi ipdelta minrho birho frac nuipmathrm wikimedia foundation powered mediawiki
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Facebook shares | Facebook likes | ||
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16 characters long
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equal found in path !
method found in path !
shares found in path !
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w httpsenwikipediaorgwindexphptitlemethodofequalsharesoldid1213284050
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http://en.wikipedia.org/static/images/icons/wikipedia.png height: 50 width: 50 description: no alt description found |
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http://en.wikipedia.org/static/images/mobile/copyright/wikipedia-wordmark-en.svg height: height attribute not set width: width attribute not set description: wikipedia |
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http://en.wikipedia.org/static/images/mobile/copyright/wikipedia-tagline-en.svg height: 13 width: 117 description: the free encyclopedia |
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https://upload.wikimedia.org/wikipedia/commons/thumb/a/ad/a_coloured_voting_box_%28no_bg%29.svg/80px-a_coloured_voting_box_%28no_bg%29.svg.png height: 80 width: 80 description: ballot box |
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https://upload.wikimedia.org/wikipedia/en/thumb/0/01/a_coloured_voting_box.svg/16px-a_coloured_voting_box.svg.png height: 16 width: 16 description: icon |
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https://upload.wikimedia.org/wikipedia/commons/thumb/e/ec/methodofequalshares-example1.png/120px-methodofequalshares-example1.png height: 94 width: 120 description: there are 9 projects. for example, the third group of 11 voters voted for d and g. the total budget of $1000 is divided equally among 100 voters. each voter is given 10. click on the arrow above the image in order to see the next steps of the method. |
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https://upload.wikimedia.org/wikipedia/commons/thumb/2/2d/methodofequalshares-example1a.png/120px-methodofequalshares-example1a.png height: 94 width: 120 description: project d obtained most votes. if we divided the cost of d equally among its supporters, each voter would pay $3.03. d is the project that minimises the maximal voter payment and so it is selected. |
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https://upload.wikimedia.org/wikipedia/commons/thumb/6/60/methodofequalshares-example1b.png/120px-methodofequalshares-example1b.png height: 94 width: 120 description: project a obtained 60 votes. analogously to the previous step: if we divided the cost of a equally among its supporters, each voter would pay at most $3.33. project a minimises the maximal voter payment and so is selected. |
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https://upload.wikimedia.org/wikipedia/commons/thumb/6/6d/methodofequalshares-example1c.png/120px-methodofequalshares-example1c.png height: 94 width: 120 description: project c obtained 56 votes and is selected in the third round. each supporter of c needs to pay $3.64, and this is the minimal possible payment. at this point the first 46 voters run out of their money. |
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https://upload.wikimedia.org/wikipedia/commons/thumb/a/ad/methodofequalshares-example1d.png/120px-methodofequalshares-example1d.png height: 94 width: 120 description: in the fourth step project g is selected. some voters do not have enough money to participate equally in the purchase, so they pay all money left. the maximal payment for this candidate equals $6.97. |
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https://upload.wikimedia.org/wikipedia/commons/thumb/7/7e/methodofequalshares-example1e.png/120px-methodofequalshares-example1e.png height: 94 width: 120 description: in the last step, project h is selected. now, only the fourth group of voters has money. they have enough money to afford the project they voted for. the maximal payment for the selected project is now $10. |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3c894024162d89aa8502758b2151cb579806ea9a height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {d} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/92b8d92a77d528d726deb4b8584ed28aea8b328e height: height attribute not set width: width attribute not set description: {\displaystyle \$200/66\approx \$3.03} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/be1811407dea8b43727d28dbe8da7251985b03e8 height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {e} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/90a0f67d48a2c34bc8503fdb0311f08004183004 height: height attribute not set width: width attribute not set description: {\displaystyle \$200/46\approx \$4.34} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/32db8e791eaa12e32afc8fc1d60386643e43e315 height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {h} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ff6366939c4ebbd4e8494d0dedc54c4b8dd7135a height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {a} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a22ea6dc0369a8826d0f3ad63159f1604ab645c6 height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {c} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/246d129731ca61aa9ff839a8d69e889746c29c9d height: height attribute not set width: width attribute not set description: {\displaystyle p=\{p_{1},p_{2},\ldots ,p_{m}\}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/46de4999ceee34d1bf6626160ea4528696de1af4 height: height attribute not set width: width attribute not set description: {\displaystyle n=\{1,2,\ldots ,n\}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f4dc1da33d78a2bdae06c9edff726feb126dae34 height: height attribute not set width: width attribute not set description: {\displaystyle p\in p} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/361cab9f7ae52869bf88f26a63d93aedf1966331 height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {cost} (p)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3 height: height attribute not set width: width attribute not set description: {\displaystyle b} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c98a794279966819df68e268cf26198f9f5b32f9 height: height attribute not set width: width attribute not set description: {\displaystyle i\in n} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/77c7e0805747f29d2eddb576eb56f7a517420c45 height: height attribute not set width: width attribute not set description: {\displaystyle u_{i}(p)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20 height: height attribute not set width: width attribute not set description: {\displaystyle i} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36 height: height attribute not set width: width attribute not set description: {\displaystyle p} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/eccf20d86205910ce97a60685e7913b3b00eda24 height: height attribute not set width: width attribute not set description: {\displaystyle b_{i}=b/n} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d8e1760b2df774fbfdc7e308dbee01418c4de105 height: height attribute not set width: width attribute not set description: {\displaystyle \rho \geq 0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64 height: height attribute not set width: width attribute not set description: {\displaystyle \rho } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/14ce7e2b47204dab98ac391b188d4a029e08a034 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}\sum _{i\in n}\min \left(b_{i},u_{i}(p)\cdot \rho \right)=\mathrm {cost} (p){\text{.}}\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ddbc84b7db4029bd4ebf37ac50c99b5406f788f7 height: height attribute not set width: width attribute not set description: {\displaystyle \textstyle \sum _{i\in n\colon u_{i}(p)>0}b_{i}<\mathrm {cost} (p){\text{.}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f1fa0d7f56592aa5c83e84b607555ccf09b7f241 height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {cost} (p)/\textstyle \sum _{i\in n}u_{i}(p)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fe702bdc96c431019e54ac6b5e6f152f64ce2f43 height: height attribute not set width: width attribute not set description: {\displaystyle b_{i}:=\max(0,b_{i}-u_{i}(p)\cdot \rho )} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/4/43/methodofequalshares-example2.png/120px-methodofequalshares-example2.png height: 92 width: 120 description: there are 8 available projects and 250 voters. for example, the first 65 voters assign value 30 to project b and value 10 to projects e and g. the total budget of $2500 is divided equally among 250 voters. each voter is given $10. click on the arrow above the image in order to see the next steps of the method. |
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https://upload.wikimedia.org/wikipedia/commons/thumb/3/3e/methodofequalshares-example2a.png/120px-methodofequalshares-example2a.png height: 92 width: 120 description: project b is selected first, and its cost is divided proportionally to the values that the voters assigned to the project. in this case, this means it is divided equally among the voters from the first and the second group. each such voter pays $2, and for those $2 they get the utility of 30. thus the maximal payment-per-utility equals '"`uniq--postmath-00000031-qinu`"'. if a different project was selected, the maximal payment-per-utility would be higher. |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0b7a2421fa6b7dff1b0ea2cbda756f8c7a22fea6 height: height attribute not set width: width attribute not set description: {\displaystyle 2/30\approx 0.066} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/d/dd/methodofequalshares-example2b.png/120px-methodofequalshares-example2b.png height: 92 width: 120 description: consider project g and the payments presented in the picture. the payments are not equal, but they are still proportional to the values that the voters' assigned to g. the maximal voter's payment-per-utility for project g equals '"`uniq--postmath-00000032-qinu`"' and this value is minimal across all projects. consequently, g is selected. after this round the voters from the fourth group have run out of money. |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4184c86535fffe374070757f1147a14b6fc6c8ca height: height attribute not set width: width attribute not set description: {\displaystyle 1/10=4/40=10/100=0.1} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/f/f5/methodofequalshares-example2c.png/120px-methodofequalshares-example2c.png height: 92 width: 120 description: in the third round project f is selected. every supporter of f pays an equal part of the price - except for voters from the fourth group, who have no money. if they had any, they would also need to participate. nevertheless, the maximal payment-per-utility for project f is minimal (it equals 0.2), hence f is elected. |
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https://upload.wikimedia.org/wikipedia/commons/thumb/4/49/methodofequalshares-example2d.png/120px-methodofequalshares-example2d.png height: 92 width: 120 description: in the fourth round, project e is elected. consider the payments presented in the picture, and note that the voters from the third group have too little money to participate in paying proportionally to their utilities, yet they all still have $4 left. in such case, they pay all money they still have. the maximal payment-per-utility (paid by the voters from the first group) is minimal, and equals circa 0.54. |
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https://upload.wikimedia.org/wikipedia/commons/thumb/6/67/methodofequalshares-example2e.png/120px-methodofequalshares-example2e.png height: 92 width: 120 description: the rule spent $2380 out of $2500 in the budget. while the voters from the first and the fifth group have positive savings, no project can be afforded by their supporters. hence the algorithm stops. the outcome can be further completed. according to the utilitarian strategy project h would be selected as its cost per utility equals '"`uniq--postmath-00000033-qinu`"' and is maximal across the projects that would fit within the budget constraint. |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d60877e62f9bbfc45ebed3ebb48b603a116ee882 height: height attribute not set width: width attribute not set description: {\displaystyle 110/(2\cdot 50+1\cdot 10+1\cdot 55)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/43d4fbe19e88e621b9e82d0b7fb3f6d89d492782 height: height attribute not set width: width attribute not set description: {\displaystyle u_{i}(p)=\mathrm {cost} (p)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8f11d349e50c8c9598e957eed7a4bd657c7ca05f height: height attribute not set width: width attribute not set description: {\displaystyle u_{i}(p)=0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5f7e539e1f68412fbfcbd11ae3bb412cbdaf151d height: height attribute not set width: width attribute not set description: {\displaystyle u_{i}(p)=1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/af5e766e923a5ba1cfc6b5ced87da468cc3ad81d height: height attribute not set width: width attribute not set description: {\displaystyle u_{i}(p)/u_{i}(p')\to \infty } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/40e623e3163571a220ed60ecb31aa78c24104b85 height: height attribute not set width: width attribute not set description: {\displaystyle p'} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3799c17934ee3c1061f221ed248a5b949dbdb513 height: height attribute not set width: width attribute not set description: {\displaystyle \succ _{i}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3d74131f4a2b917445d3ff022c4f1200997b9821 height: height attribute not set width: width attribute not set description: {\displaystyle y\succ _{i}x\succ _{i}z} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab height: height attribute not set width: width attribute not set description: {\displaystyle x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1cc6b75e09a8aa3f04d8584b11db534f88fb56bd height: height attribute not set width: width attribute not set description: {\displaystyle z} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ae8fe32f08e054491580952a13026532294a4e5f height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {pos} _{i}(y)=1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0b7e424021a7198611124cfd5f2f3c6a54aa164b height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {pos} _{i}(x)=2} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1c81e52b2492c12289f652f9c97000a02fd760bb height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {pos} _{i}(z)=3} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c5321cfa797202b3e1f8620663ff43c4660ea03a height: height attribute not set width: width attribute not set description: {\displaystyle \delta } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/04c939bbaaee9b6befd475cc18ea7a2f60a99c96 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}\sum _{i\in n\colon \mathrm {pos} _{i}(p)\leq \delta }b_{i}\geq \mathrm {cost} (p){\text{.}}\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fee982a415ff3fb0e06e0c170a7f54df26d38b83 height: height attribute not set width: width attribute not set description: {\displaystyle \textstyle \sum _{i\in n}b_{i}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2171efc20e6529920b7d57cea7ec380089b91143 height: height attribute not set width: width attribute not set description: {\displaystyle \delta :=1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/50cebc43846886435ddd0447a981a83209f6303e height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {cost} :=\mathrm {cost} (p)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/29812f830889414a7f38f8bb92e600df0914a1e4 height: height attribute not set width: width attribute not set description: {\displaystyle \textstyle \sum _{i\in n\colon \mathrm {pos} _{i}(p)=\delta }b_{i}\geq \mathrm {cost} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d23d24995f16cb139544ae1bdcf94fd06c5de0b3 height: height attribute not set width: width attribute not set description: {\displaystyle \textstyle \sum _{i\in n\colon \mathrm {pos} _{i}(p)=\delta }\min(\rho ,b_{i})=\mathrm {cost} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1bb27151d0775a18a0f8baceb2be8d3b1416f6b3 height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {pos} _{i}(p)=\delta } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f5ab9d063f0eacc1bfa9274022bb4e98c1c4917e height: height attribute not set width: width attribute not set description: {\displaystyle b_{i}:=\max(0,b_{i}-\rho )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ef174d90efb15285970d950be691e5124fcdd690 height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {cost} :=\mathrm {cost} -\textstyle \sum _{i\in n\colon \mathrm {pos} _{i}(p)=\delta }b_{i}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b30d51744b0f44182d503b4e9aa15c078753831b height: height attribute not set width: width attribute not set description: {\displaystyle b_{i}:=0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9bd073953e15aef3e2f63383ccbd4e34fb83440a height: height attribute not set width: width attribute not set description: {\displaystyle \delta :=\delta +1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/72421845401745458bbe2be4a4c3ac8960570028 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {\sum _{i\in n}u_{i}(p)}{\mathrm {cost} (p)}}} |
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https://login.wikimedia.org/wiki/special:centralautologin/start?type=1x1 height: 1 width: 1 description: no alt description found |
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http://en.wikipedia.org/static/images/footer/wikimedia-button.png height: 31 width: 88 description: wikimedia foundation |
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http://en.wikipedia.org/static/images/footer/poweredby_mediawiki_88x31.png height: 31 width: 88 description: powered by mediawiki |
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