Zhihao Gavin Tang

How to match when all vertices arrive online

We introduce a fully online model of maximum cardinality matching in which all vertices arrive online. On the arrival of a vertex, its incident edges to previously-arrived vertices are revealed. Each vertex has a deadline that is after all its neighbors’ arrivals. If a vertex remains unmatched until its deadline, the algorithm must then irrevocably either match it to an unmatched neighbor, or leave it unmatched. The model generalizes the existing one-sided online model and is motivated by applications including ride-sharing platforms, real-estate agency, etc. We show that the Ranking algorithm by Karp et al. (STOC 1990) is 0.5211-competitive in our fully online model for general graphs. Our analysis brings a novel charging mechanic into the randomized primal dual technique by Devanur et al. (SODA 2013), allowing a vertex other than the two endpoints of a matched edge to share the gain. To our knowledge, this is the first analysis of Ranking that beats 0.5 on general graphs in an online matching problem, a first step towards solving the open problem by Karp et al. (STOC 1990) about the optimality of Ranking on general graphs. If the graph is bipartite, we show that the competitive ratio of Ranking is between 0.5541 and 0.5671. Finally, we prove that the fully online model is strictly harder than the previous model as no online algorithm can be 0.6317 < 1−1/e-competitive in our model even for bipartite graphs.

Online Submodular Maximization Problem with Vector Packing Constraint

We consider the online vector packing problem in which we have a

Online Vertex-Weighted Bipartite Matching: Beating 1-1/e with Random Arrivals

d

Online Submodular Maximization with Free Disposal

dimensional knapsack and items

Online submodular maximization with free disposal: randomization beats 1/4 for partition matroids

u

On (1, epsilon)-Restricted Max-Min Fair Allocation Problem

with weight vectors

On (1, \(\epsilon \))-Restricted Max–Min Fair Allocation Problem

\mathbf{w}_u \in \mathbb{R}_+^d

Diffusion Operator and Spectral Analysis for Directed Hypergraph Laplacian.

arrive online in an arbitrary order. Upon the arrival of an item, the algorithm must decide immediately whether to discard or accept the item into the knapsack. When item

The value of information concealment

u

Online Makespan Minimization: The Power of Restart.

is accepted,