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- W2999309755 abstract "We study two aspects of the complexity of counting the number of t-cliques in a graph: 1) Worst-case to reductions: Our main result reduces counting t-cliques in any n-vertex graph to counting t-cliques in typical n-vertex graphs that are drawn from a simple distribution of min-entropy Ω(n^2). For any constant t, the reduction runs in O(n^2)-time, and yields a correct answer (w.h.p.) even when the average-case solver only succeeds with probability 1/(polylog n). 2) Direct interactive proof systems: We present a direct and simple interactive proof system for counting t-cliques in n-vertex graphs. The proof system uses (t-2) rounds, the verifier runs in O(t^2 n^2)-time, and the prover can be implemented in O(t^O(1) n^2)-time when given oracle access to counting (t-1)-cliques in O(t^O(1) n)-vertex graphs. The results are both obtained by considering weighted versions of the t-clique problem, where weights are assigned to vertices and/or to edges, and the weight of cliques is defined as the product of the corresponding weights. These weighted problems are shown to be easily reducible to the unweighted problem." @default.
- W2999309755 created "2020-01-23" @default.
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- W2999309755 date "2018-01-01" @default.
- W2999309755 modified "2023-09-28" @default.
- W2999309755 title "Counting t -cliques: Worst-case to average-case reductions and Direct interactive proof systems." @default.
- W2999309755 hasPublicationYear "2018" @default.
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