Fast Retrieval Algorithm for Earth Mover's Distance Using EMD Lower Bounds and a Skipping Algorithm

<table class="table-group" id="tab4"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td align="left"></td><td align="center">Weight</td><td align="center"><span style="width: 8.7250004px;"><svg height="7.1624999" id="M110" style="vertical-align:-0.11285pt" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.1625)">
<g transform="translate(72,-66.27)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑥</tspan>
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</svg></span></td><td align="center"><span style="width: 7.875px;"><svg height="9.8625002" id="M111" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 7.875 9.8625002" width="7.875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.8625)">
<g transform="translate(72,-64.11)">
<text transform="matrix(1,0,0,-1,-71.95,66.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑦</tspan>
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</svg></span></td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td align="left"><span style="width: 16.700001px;"><svg height="14.4875" id="M112" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 16.700001 14.4875" width="16.700001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.4875)">
<g transform="translate(72,-60.41)">
<text transform="matrix(1,0,0,-1,-71.95,63.71)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐶</tspan>
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<text transform="matrix(1,0,0,-1,-63.56,60.58)">
<tspan style="font-size: 8.75px; " x="0" y="0">0</tspan>
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</svg></span></td><td align="center">0.5</td><td align="center">5</td><td align="center">5</td></tr><tr><td align="left"><span style="width: 16.700001px;"><svg height="14.3375" id="M113" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 16.700001 14.3375" width="16.700001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.3375)">
<g transform="translate(72,-60.53)">
<text transform="matrix(1,0,0,-1,-71.95,63.71)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐶</tspan>
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<text transform="matrix(1,0,0,-1,-63.56,60.58)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center">0.5</td><td align="center">5</td><td align="center">0</td></tr><tr><td align="left"><span style="width: 16.700001px;"><svg height="14.3375" id="M114" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 16.700001 14.3375" width="16.700001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.3375)">
<g transform="translate(72,-60.53)">
<text transform="matrix(1,0,0,-1,-71.95,63.71)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐶</tspan>
</text>
<text transform="matrix(1,0,0,-1,-63.56,60.58)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center">0.2</td><td align="center">2</td><td align="center">7</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

An example of the signature <svg height="10.6125" id="M109" style="vertical-align:-0.15048pt" version="1.1" viewbox="0 0 11.8625 10.6125" width="11.8625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.6125)">
<g transform="translate(72,-63.51)">
<text transform="matrix(1,0,0,-1,-71.95,63.71)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐶</tspan>
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tab4

Table 4

Table 4: Fast Retrieval Algorithm for Earth Mover's Distance Using EMD Lower Bounds and a Skipping Algorithm 