data/220.json
{
"definitions": {
"c_{i}": [
"cost of broadcasting a unit-rate flow (one packet per unit time)",
{}
],
"t": [
"unicast flow",
{}
],
"T": [
"set of unicast flows",
{
"Q36161": "set"
}
],
"i": [
{
"Q2303886": "index"
}
],
"j": [
{
"Q2303886": "index"
}
],
"v": [
{
"Q2303886": "index"
}
],
"w": [
{
"Q2303886": "index"
}
],
"\\mathcal{N}": [
{
"Q28920044": "positive integer"
}
],
"L": [
"Lagrangian density",
{
"Q505735": "Lagrangian"
}
],
"p": [
{
"Q598870": "Lagrange multiplier"
}
],
"x": [
{
"Q44528": "vector",
"Q192388": "position vector"
}
],
"y": [
{
"Q44528": "vector",
"Q192388": "position vector"
}
],
"Gamma_{G^{\\prime}}": [
"set of all triples of connected nodes on the expanded graph Gā²",
{}
]
},
"constraints": [],
"math_inputtex": "L(\\boldsymbol{x},\\boldsymbol{y},\\boldsymbol{p})=\\sum_{i\\in\\mathcal{N}}\\sum_{v<% w:(v,i,w)\\in\\Gamma_{G^{\\prime}}}\\bigg{[}c_{i}y^{i}_{vw}+p(v,i,w)\\Big{(}\\sum_{t% \\in T}x^{t}(v,i,w)-y^{i}_{vw}\\Big{)}+p(w,i,v)\\Big{(}\\sum_{t\\in T}x^{t}(w,i,v)-% y^{i}_{wv}\\Big{)}\\bigg{]}.",
"math_inputtex_semantic": "\\wf{Q505735}{L}(\\w{Q192388}{\\boldsymbol{x}},\\w{Q192388}{\\boldsymbol{y}},\\w{Q44528}{\\boldsymbol{p}})=\\sum_{\\w{Q2303886}{i} \\in \\w{Q28920044}{\\mathcal{N}}}\\sum_{\\w{Q2303886}{v}<\\w{Q2303886}{w}: (v,i,w)\\in\\Gamma_{G^{\\prime}}}\\bigg{[} \\w{Q50700}{c}_{i}y^{i}_{vw} + \\wf{Q44528}{p}(v,i,w)\\Big{(}\\sum_{\\w{Q379825}{t} \\in \\w{Q36161}{T}}x^{t}(v,i,w)-y^{i}_{vw}\\Big{)}+\\wf{Q44528}{p}(w,i,v)\\Big{(}\\sum_{t\\in T}x^{t}(w,i,v) - y^{i}_{wv}\\Big{)}\\bigg{]}",
"correct_tex": "L(\\boldsymbol{x},\\boldsymbol{y},\\boldsymbol{p}) = \\sum_{i \\in \\mathcal{N}} \\sum_{v<w:(v,i,w)\\in\\Gamma_{G^{\\prime}}} [c_{i}y^{i}_{vw}+p(v,i,w) (\\sum_{t \\in T}x^{t}(v,i,w)-y^{i}_{vw}) + p(w,i,v) (\\sum_{t\\in T}x^{t}(w,i,v)-y^{i}_{wv})]",
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id=\"p1.1.m1.1c\">L(\\boldsymbol{x},\\boldsymbol{y},\\boldsymbol{p})=\\sum_{i\\in\\mathcal{N}}\\sum_{v<%\nw:(v,i,w)\\in\\Gamma_{G^{\\prime}}}\\bigg{[}c_{i}y^{i}_{vw}+p(v,i,w)\\Big{(}\\sum_{t%\n\\in T}x^{t}(v,i,w)-y^{i}_{vw}\\Big{)}+p(w,i,v)\\Big{(}\\sum_{t\\in T}x^{t}(w,i,v)-%\ny^{i}_{wv}\\Big{)}\\bigg{]}</annotation>\n </semantics>\n</math>\n",
"uri": "https://arxiv.org/abs/1001.3171",
"title": "Use of Lagrange multipliers",
"comment": "recompiled because original formula was in multiline eqnarray",
"type": "equation",
"ntcir12-type": "20",
"formula": "1_17",
"page": "3",
"ntcir12-relevance": "4"
}