Proximity Search for Maximal Subgraph Enumeration

This paper proposes a new general technique for maximal subgraph enumeration which we call proximity search, whose aim is to design efficient algorithms problems that could not be solved by existing frameworks. To support this claim and illustrate the include output-polynomial several were known, including of bipartite subgraphs, -degenerate subgraphs (for bounded ), induced chordal trees. Using known techniques, such as reverse space all solutions induces an implicit directed graph called “solution graph” or “supergraph,” are enumerated traversing it; however, nodes in can have exponential out-degree, thus requiring time spent on each solution. The novelty search formalization allows us define better solution graph, technique, canonical reconstruction, exploit properties given build graphs. results graphs significantly smaller (i.e., polynomial) out-degree with respect approaches, but remain strongly connected, so polynomial delay traversal. A drawback approach required keep track visited solutions, exponential; further propose induce parent-child relationship among achieve when suitable conditions met.