and Edge Arrival Models Nick Gravin Tomer Ezra Michal Feldman - PowerPoint PPT Presentation

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Prophet Inequality for Vertex and Edge Arrival Models Nick Gravin Tomer Ezra Michal Feldman Zhihao Gavin Tang Shanghai University of Tel Aviv University and Shanghai University of Tel Aviv University Finance and Economics Microsoft

Prophet Inequality for Vertex and Edge Arrival Models Nick Gravin Tomer Ezra Michal Feldman Zhihao Gavin Tang Shanghai University of Tel Aviv University and Shanghai University of Tel Aviv University Finance and Economics Microsoft Research Finance and Economics
Prophet Inequality for Matching • G =(V,E): general weighted graph • Weight of Edge e, 𝑥 𝑓 , is drawn independently from a known distribution 𝐺 𝑓 • Elements arrive online, weights are revealed upon arrival • Online selection (immediate and irrevocable): a matching 𝑁 ⊂ 𝐹 • Goal : Pick maximum weighted matching 𝑁
Two Variants of Matching Prophet Inequality Vertex arrival : Edge arrival : • Vertices arrive one by one • Edges arrive one by one (arbitrary (arbitrary order) order) • Upon arrival, weights of edges to all • Upon arrival, edge ’ s weight is revealed previous vertices are revealed 1 𝑥 𝑓2 = 0.6 𝑉[0,3] 2 3
Our Results Edge arrival : Vertex arrival : • 0.337 approximation • ½ approximation - tight 1 • Unknown arrival order • Improves upon 3 -approximation of • General graphs [Gravin, Wang EC19] • G eneral graphs • In paper: a general framework for batched prophet inequality • elements arrive in batches (e.g., vertex arrival)

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