Optimization, approximation, and complexity classes
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
The approximability of NP-hard problems
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
A new average case analysis for completion time scheduling
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Random Structures & Algorithms
Combinatorics, Probability and Computing
Combinatorica
Delaying satisfiability for random 2SAT
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Small subgraphs in random graphs and the power of multiple choices
Journal of Combinatorial Theory Series B
Connected components and evolution of random graphs: an algebraic approach
Journal of Algebraic Combinatorics: An International Journal
Publish-subscribe systems via gossip: a study based on complex networks
Proceedings of the Fourth Annual Workshop on Simplifying Complex Networks for Practitioners
An analysis of one-dimensional schelling segregation
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Gossiping for resource discovering: An analysis based on complex network theory
Future Generation Computer Systems
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Consider a game in which edges of a graph are provided a pair at a time, and the player selects one edge from each pair, attempting to construct a graph with a component as large as possible. This game is in the spirit of recent papers on avoiding a giant component, but here we embrace it. We analyze this game in the offline and online setting, for arbitrary and random instances, which provides for interesting comparisons. For arbitrary instances, we find that the competitive ratio (the best possible solution value divided by best possible online solution value) is large. For "sparse" random instances the competitive ratio is also large, with high probability (whp): If the instance has 1/4(1 + ε)n random edge pairs, with 0 O((log n)3/2) whp, while the optimal offline solution contains a component of size Ω(n) whp. For "dense" random instances, the average-case competitive ratio is much smaller. If the instance has ½(1 - ε)n random edge pairs, with 0 n) whp.