You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
For some computational problems (e.g., product configuration, planning, diagnosis, query answering, phylogeny reconstruction) computing a set of similar diverse solutions may be desirable for better decision-making. With this motivation, we studied several decision optimization versions of this problem in the context of Answer Set Programming (ASP), analyzed their computational complexity, and introduced offline online methods to compute similar diverse solutions of such computational problems with respect to a given distance function. All these methods rely on the idea of computing solutions to a problem by means of finding the answer sets for an ASP program that describes the problem. The offline methods compute all solutions in advance using the ASP formulation of the problem with an ASP solver, like Clasp, and then identify similar diverse solutions using clustering methods. The online methods compute similar diverse solutions following one of the three approaches: by reformulating the ASP representation of the problem to compute similar diverse solutions at once using an ASP solver; by computing similar diverse solutions iteratively (one after other) using an ASP solver; by modifying the search algorithm of an ASP solver to compute similar diverse solutions incrementally. We modified Clasp to implement the last online method and called it Clasp-NK. In the first two online methods, the given distance function is represented in ASP; in the last one it is implemented in C++. We showed the applicability and the effectiveness of these methods on reconstruction of similar diverse phylogenies for Indo-European languages, and on several planning problems in Blocks World. We observed that in terms of computational efficiency the last online method outperforms the others; also it allows us to compute similar diverse solutions when the distance function cannot be represented in ASP.

Cited Abstract(s):
[1]: It is useful in a wide range of situations to find solutions which are diverse (or similar) to each other. We therefore define a number of different classes of diversity and similarity problems. For example, what is the most diverse set of solutions of a constraint satisfaction problem with a given cardinality? We first determine the computational complexity of these problems. We then propose a number of practical solution methods, some of which use global constraints for enforcing diversity (or similarity) between solutions. Empirical evaluation on a number of problems show promising results.
which are similar to @math -distant set (resp. @math -close set ): [1] asks for a set of @math solutions @math -distant close to one solution, whereas @math -distant close set asks for a set of solutions that is @math -close distant to a set of previously computed solutions. Also, the distance measure considered in @math Distant @math Set (resp. @math Close @math Set ) is computable in polynomial time; in @math -distant set (resp. @math -close set ) deciding whether the distance of a set of solutions is less than a given @math is assumed to be in .