Internet users constantly make searches to find objects or results of their interest, generally through terms or phrases. Traditional search offers only solutions that take into account just the individual characteristics of the results, and not the relations they have with the rest of the universe. Typically, we are given an ordered list of the results related to the search criterion, which implies the need of changing several times the terms of the query to get to a solution that is more adequate to the intended search goal. As a solution to this problem, Composite Retrieval proposes that the results to a query may be grouped in sets of items (bundles), related through some similarity criterion, but at the same time are complementary. In this work we propose heuristic algorithms for Composite Retrieval which are evaluated experimentally, showing performance improvements over the previous results presented in the literature.

In this article, we study the (k,c)‐coloring problem, a generalization of the vertex coloring problem where we have to assign k colors to each vertex of an undirected graph, and two adjacent vertices can share at most c colors. We propose a new formulation for the (k,c)‐coloring problem and develop a Branch‐and‐Price algorithm. We tested the algorithm on instances having from 20 to 80 vertices and different combinations for k and c, and compare it with a recent algorithm proposed in the literature. Computational results show that the overall approach is effective and has very good performance on instances where the previous algorithm fails. © 2014 Wiley Periodicals, Inc. NETWORKS, 2014 Vol. 65(4), 353–366 2015

Users are often faced with the problem of finding complementary items that together achieve a single common goal (e.g., a starter kit for a novice astronomer, a collection of question/answers related to low-carb nutrition, a set of places to visit on holidays). In this paper, we argue that for some application scenarios returning item bundles is more appropriate than ranked lists. Thus we define composite retrieval as the problem of finding$k$bundles of complementary items. Beyond complementarity of items, the bundles must be valid w.r.t. a given budget, and the answer set of$k$bundles must exhibit diversity. We formally define the problem and show that in its general form is${\bf NP}$-hard and that also the special cases in which each bundle is formed by only one item, or only one bundle is sought, are hard. Our characterization however suggests how to adopt a two-phase approach (Produce-and-Choose, or PAC) in which we first produce many valid bundles, and then we choose$k$among them. For the first phase we devise two ad-hoc clustering algorithms, while for the second phase we adapt heuristics with approximation guarantees for a related problem. We also devise another approach which is based on first finding a$k$-clustering and then selecting a valid bundle from each of the produced clusters (Cluster-and-Pick, or CAP). We compare experimentally the proposed methods on two real-world data sets: the first data set is given by a sample of touristic attractions in 10 large European cities, while the second is a large database of user-generated restaurant reviews from Yahoo! Local. Our experiments show that when diversity is highly important, CAP is the best option, while when diversity is less important, a PAC approach constructing bundles around randomly chosen pivots, is better.