Faster Graph Coloring in Polynomial Space

Abstract We present a polynomial-space algorithm that computes the number of independent sets any input graph in time $$O(1.1389^n)$$ O ( 1 . 1389 n ) for graphs with maximum degree 3 and $$O(1.2356^n)$$ 2356 general graphs, where n is vertices graph. Together inclusion-exclusion approach Björklund, Husfeldt, Koivisto [SIAM J. Comput. 2009], this leads to faster coloring problem running $$O(2.2356^n)$$ 2 as well an exponential-space $$O(1.2330^n)$$ 2330 counting sets. Our main counts at most no vertex three neighbors 3. This designed analyzed using recently introduced Separate, Measure Conquer [Gaspers & Sorkin, ICALP 2015]. Using Wahlström’s compound measure approach, improvement small then bootstrapped larger degrees, giving graphs. Combining both approaches some inflexibility choosing branch on small-degree cases, which we counter by structural properties.