Random 2-SAT with Prescribed Literal Degrees

Two classic “phase transitions” in discrete mathematics are the emergence of a giant component in a random graph as the density of edges increases, and the transition of a random 2-SAT formula from satisfiable to unsatisfiable as the density of clauses increases. The randomgraph result has been extended to the case of prescribed degree sequences, where the almostsure nonexistence or existence of a giant component is related to a simple property of the degree sequence. We similarly extend the satisfiability result, by relating the almost-sure satisfiability or unsatisfiability of a random 2-SAT formula to an analogous property of its prescribed literal-degree sequence. The extension has proved useful in analyzing literal-degree-based algorithms for (uniform) random 3-SAT.

• Type: Journal
• Year: 2007
• Where: ALGORITHMICA
• Authors: Colin Cooper, Alan M. Frieze, Gregory B. Sorkin
• Keywords: ALGORITHMICA 2007, Degree Sequence, Giant Component, Random 2-SAT Formula