Sublinear-Time Algorithms for Max Cut, Max E2Lin(q), and Unique Label Cover on Expanders

We show sublinear-time algorithms for MAX CUT and MAX E2LIN(q) on expanders in the adjacency list model that distinguishes instances with the optimal value more than 1 − ε from those with the optimal value less than 1 − ρ for ρ ≫ ε. The time complexities for MAX CUT and MAX 2LIN(q) are and , respectively, where m is the number of edges in the underlying graph and ϕ is its conductance. Then, we show a sublinear-time algorithm for UNIQUE LABEL COVER on expanders with ϕ ≫ ε in the bounded-degree model. The time complexity of our algorithm is Õd(2qO(1)·ϕ1/q·ε-1/2 · n1/2+qO(q)·ε41.5-q ·ϕ-2), where n is the number of variables. We complement these algorithmic results by showing that testing 3-colorability requires Ω(n) queries even on expanders.