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Table of contents
1 Introduction
1.1 Notions of graph theory
1.2 Load-balancing problems
1.3 Introduction to the cavity method
1.4 Overview of the results
2 Maximum capacitated matching via the cavity method
2.1 Introduction
2.2 Asymptotic size of maximum capacitated matchings
2.3 Main proof elements
2.4 Structural properties of local operators
2.5 Finite graphs
2.6 Limit of large graphs
2.7 Exactness in finite bipartite graphs
3 Cuckoo hashing thresholds
3.1 Introduction
3.2 Cuckoo hashing threshold and hypergraph orientability
3.3 An analysis of double hashing
4 Load-balancing and resource-placement in distributed CDNs
4.1 Introduction
4.2 Edge-assisted CDN model and statistical assumptions
4.3 Related models and replication strategies
4.4 Performance under optimal matching
4.5 Performance under random greedy matching
4.6 Adaptive replication schemes to minimize losses
