"Search is a problem-solving technique that systematically explores a space of problem states, i.e., successive and alternative stages in the problem-solving process. Examples of problem states might include the different board configurations in a game or intermediate steps in a reasoning process. This space of alternative solutions is then searched to find an answer. Newell and Simon (1976) have argued that this is the essential basis of human problem solving. Indeed, when a chess player examines the effects of different moves or a doctor considers a number of alternative diagnoses, they are searching among alternatives." – from Section 1.2 of Chapter One of George F. Luger's textbook, Artificial Intelligence: Structures and Strategies for Complex Problem Solving, 5th Edition (Addison-Wesley; 2005).
To this end, we first establish a new class of GNNs that can solve a strictly wider variety of problems than existing GNNs. Then, we bridge the gap between GNN theory and the theory of distributed local algorithms.
Successfully employing cutting planes can be challenging because there are infinitely many cuts to choose from and there are still many open questions about which cuts to employ when.