powerpoint presentationaghazima/azin-files/wsdm/prince-ws… · title: powerpoint presentation...

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★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ = ,, ,,, ∗ , ∗ ∗ ← , ∗ ← ∈ = , , , < ∗ ∗ ← , ∗ ← ∗ , ∗ ★ ★ ★ ★ ← , , ∗ ← , ← 0, ← () , ∈ ← , × , − ( , ∗ |)] . ( , ) ← + > 0 , ← . _max() ← − ∗ ← ∗ ∪ (, ) ∗ ( × × log ||) Underlying Theorem: , ∗ ) < , ∗ | ∗ ⇔ , ∈\ ∗ , ⋅ , − , ∗ <

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Page 1: PowerPoint Presentationaghazima/Azin-files/wsdm/prince-ws… · Title: PowerPoint Presentation Author: Administrator Created Date: 1/31/2020 10:04:18 AM

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𝐺 = 𝑉, 𝐸, 𝜃 , 𝑢, 𝑟𝑒𝑐, 𝐼

𝐴∗, 𝑟𝑒𝑐∗

𝐴∗ ← 𝐴, 𝑟𝑒𝑐∗ ← 𝑟𝑒𝑐

𝑖 ∈ 𝐼

𝐴𝑖 = 𝑆𝑤𝑎𝑝𝑂𝑟𝑑𝑒𝑟 𝐺, 𝑢, 𝑟𝑒𝑐, 𝑖

𝐴𝑖 < 𝐴∗

𝐴∗ ← 𝐴𝑖 , 𝑟𝑒𝑐∗ ← 𝑖

𝐴∗, 𝑟𝑒𝑐∗

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𝐴 ← 𝐴𝑙𝑙 𝑢, 𝑛𝑖 , 𝐴∗← 𝜙, 𝑠𝑢𝑚 ← 0,𝐻 ← 𝑀𝑎𝑥𝐻𝑒𝑎𝑝()

𝑢, 𝑛𝑖 ∈ 𝐴

𝑑𝑖𝑓𝑓 ← 𝑊 𝑢, 𝑛𝑖 × 𝑃𝑃𝑅 𝑛𝑖 , 𝑟𝑒𝑐 𝐴 − 𝑃𝑃𝑅(𝑛𝑖 , 𝑟𝑒𝑐∗|𝐴)]

𝐻. 𝑖𝑛𝑠𝑒𝑟𝑡(𝑛𝑖 , 𝑑𝑖𝑓𝑓)

𝑠𝑢𝑚 ← 𝑠𝑢𝑚 + 𝑑𝑖𝑓𝑓

𝑠𝑢𝑚 > 0

𝑛𝑖 , 𝑑𝑖𝑓𝑓 ← 𝐻. 𝑑𝑒𝑙𝑒𝑡𝑒_max()

𝑠𝑢𝑚 ← 𝑠𝑢𝑚 − 𝑑𝑖𝑓𝑓

𝐴∗ ← 𝐴∗ ∪ (𝑢, 𝑛𝑖)

𝐴∗

𝑂( 𝐼 × 𝐴 × log |𝐴|)

Underlying Theorem: 𝑷𝑷𝑹 𝒖, 𝒓𝒆𝒄 𝑨∗) < 𝑷𝑷𝑹 𝒖, 𝒓𝒆𝒄∗|𝑨∗ ⇔ 𝒖,𝒏𝒊 ∈𝑨\𝑨∗𝑾 𝒖,𝒏𝒊 ⋅ 𝑷𝑷𝑹 𝒏𝒊, 𝒓𝒆𝒄 𝑨 − 𝑷𝑷𝑹 𝒏𝒊, 𝒓𝒆𝒄

∗ 𝑨 < 𝟎

𝑆𝑤𝑎𝑝𝑂𝑟𝑑𝑒𝑟

mailto:[email protected]

mailto:[email protected]

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