CliSAT: A new exact algorithm for hard maximum clique problems

CliReg: Clique-based robust Point Cloud Registration

“…• An algorithm CliReg that efficiently implements the methodology mentioned above is described. At the core of CliReg lies a very efficient BnB clique algorithm that incrementally enumerates maximal cliques in our correspondence graph and builds on cutting-edge optimization techniques employed by recent efficient algorithms for the Maximum Clique Problem [58,59,57,60,62,61,44,65].…”

“…The 3 main components of CliReg are the following: i) Initialization: For the two given point clouds M, Q, a correspondence set C is determined based on local features, and a correspondence graph G is built according to Section IV-B. ii) Enumeration: maximal cliques in G are enumerated with a maximum clique algorithm that uses the latest optimization techniques (see, e.g., [58,59,57,60,62,61,44,65]) and is specifically designed for this problem. iii) Consensus: each maximal k-clique enumerated in ii) is evaluated under the assumption that it refers to a (valid) set of k inliers as follows: a) rotation and translation are estimated by solving the least-squares formulation (2), and b) for the resulting transformation, Constraints (4) are checked to determine the real number of inliers in C. The algorithm CliReg returns the maximal clique enumerated in ii) with the maximum consensus.…”

“…Reformulating the MC problem as a tailored maximum clique search has the following advantages: i) it is able to exploit most of the optimization techniques of today's efficient MCP algorithms, which have improved greatly in the last two decades, see, e.g., [58,59,57,60,62,61] and especially [44,65]. ii) as argued in Section V, solving the least-squares optimization problem (2) for every node in the branching tree is inefficient.…”

“…Consequently, MaxClqReg branches on the vertices in the branching set B. Furthermore, and in order to reduce the size of the branching tree, the set B should be as small as possible (alternatively P as large as possible); see, e.g., [44,65]; so the ideal set P is the solution to the following optimization problem:…”

“…Partial maximum satisfiability-based bounds were allegedly first proposed for the MCP in [42]. Examples of efficient MCP algorithms that employ either one or both bounds as bounding functions to partition the candidate set of vertices are [45,46,57,58,59,60,63,62,64], and also today's state-of-the-art algorithms [44,65]. We refer the interested reader to the cited literature for further details.…”