## SFS: Similarity-First Search Seriation Algorithm

An implementation of the Similarity-First Search algorithm (SFS), a combinatorial algorithm which can be used to solve the seriation problem and to recognize some structured weighted graphs. The SFS algorithm represents a generalization to weighted graphs of the graph search algorithm Lexicographic Breadth-First Search (Lex-BFS), a variant of Breadth-First Search. The SFS algorithm reduces to Lex-BFS when applied to binary matrices (or, equivalently, unweighted graphs). Hence this library can be also considered for Lex-BFS applications such as recognition of graph classes like chordal or unit interval graphs. In fact, the SFS seriation algorithm implemented in this package is a multisweep algorithm, which consists in repeating a finite number of SFS iterations (at most n sweeps for a matrix of size n). If the data matrix has a Robinsonian structure, then the ranking returned by the multistep SFS algorithm is a Robinson ordering of the input matrix. Otherwise the algorithm can be used as a heuristic to return a ranking partially satisfying the Robinson property.

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