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.
Considering partial Hamming distance as in @cite_24 , present an offline method (similar to our method) that applies clustering methods, and two online methods: one based on reformulation (similar to Online Method 1), the other based on a greedy algorithm (similar to Online Method 2) that iteratively computes a solution that maximizes similarity to previous solutions. The computation of a @math -close solution is due to a Branch & Bound algorithm (similar to the idea behind Online Method 3) that propagates some similarity diversity constraints specific to the given distance function. Our offline online methods are inspired by these methods of @cite_31 @cite_23 .
@cite_24 @cite_31 @cite_23
2099812803 2069278600 1964858027 2100839471
We introduce a new probabilistic proximity search algorithm for range and A"-nearest neighbor (A"-NN) searching in both coordinate and metric spaces. Although there exist solutions for these problems, they boil down to a linear scan when the space is intrinsically high dimensional, as is the case in many pattern recognition tasks. This, for example, renders the A"-NN approach to classification rather slow in large databases. Our novel idea is to predict closeness between elements according to how they order their distances toward a distinguished set of anchor objects. Each element in the space sorts the anchor objects from closest to farthest to it and the similarity between orders turns out to be an excellent predictor of the closeness between the corresponding elements. We present extensive experiments comparing our method against state-of-the-art exact and approximate techniques, both in synthetic and real, metric and nonmetric databases, measuring both CPU time and distance computations. The experiments demonstrate that our technique almost always improves upon the performance of alternative techniques, in some cases by a wide margin. We present a new efficient algorithm for the search version of the approximate Closest Vector Problem with Preprocessing (CVPP). Our algorithm achieves an approximation factor of O(n sqrt log n ), improving on the previous best of O(n^ 1.5 ) due to Lag arias, Lenstra, and Schnorr hkzbabai . We also show, somewhat surprisingly, that only O(n) vectors of preprocessing advice are sufficient to solve the problem (with the slightly worse approximation factor of O(n)). We remark that this still leaves a large gap with respect to the decisional version of CVPP, where the best known approximation factor is O(sqrt n log n ) due to Aharonov and Regev AharonovR04 . To achieve these results, we show a reduction to the same problem restricted to target points that are close to the lattice and a more efficient reduction to a harder problem, Bounded Distance Decoding with preprocessing (BDDP). Combining either reduction with the previous best-known algorithm for BDDP by Liu, Lyubashevsky, and Micciancio LiuLM06 gives our main result. In the setting of CVP without preprocessing, we also give a reduction from (1+eps)gamma approximate CVP to gamma approximate CVP where the target is at distance at most 1+1 eps times the minimum distance (the length of the shortest non-zero vector) which relies on the lattice sparsification techniques of Dadush and Kun DadushK13 . As our final and most technical contribution, we present a substantially more efficient variant of the LLM algorithm (both in terms of run-time and amount of preprocessing advice), and via an improved analysis, show that it can decode up to a distance proportional to the reciprocal of the smoothing parameter of the dual lattice MR04 . We show that this is never smaller than the LLM decoding radius, and that it can be up to an wide tilde Omega (sqrt n ) factor larger. Scalable image search based on visual similarity has been an active topic of research in recent years. State-of-the-art solutions often use hashing methods to embed high-dimensional image features into Hamming space, where search can be performed in real-time based on Hamming distance of compact hash codes. Unlike traditional metrics (e.g., Euclidean) that offer continuous distances, the Hamming distances are discrete integer values. As a consequence, there are often a large number of images sharing equal Hamming distances to a query, which largely hurts search results where fine-grained ranking is very important. This paper introduces an approach that enables query-adaptive ranking of the returned images with equal Hamming distances to the queries. This is achieved by firstly offline learning bitwise weights of the hash codes for a diverse set of predefined semantic concept classes. We formulate the weight learning process as a quadratic programming problem that minimizes intra-class distance while preserving inter-class relationship captured by original raw image features. Query-adaptive weights are then computed online by evaluating the proximity between a query and the semantic concept classes. With the query-adaptive bitwise weights, returned images can be easily ordered by weighted Hamming distance at a finer-grained hash code level rather than the original Hamming distance level. Experiments on a Flickr image dataset show clear improvements from our proposed approach. With the proliferation of images on the Web, fast search of visually similar images has attracted significant attention. State-of-the-art techniques often embed high-dimensional visual features into low-dimensional Hamming space, where search can be performed in real-time based on Hamming distance of compact binary codes. Unlike traditional metrics (e.g., Euclidean) of raw image features that produce continuous distance, the Hamming distances are discrete integer values. In practice, there are often a large number of images sharing equal Hamming distances to a query, resulting in a critical issue for image search where ranking is very important. In this paper, we propose a novel approach that facilitates query-adaptive ranking for the images with equal Hamming distance. We achieve this goal by firstly offline learning bit weights of the binary codes for a diverse set of predefined semantic concept classes. The weight learning process is formulated as a quadratic programming problem that minimizes intra-class distance while preserving interclass relationship in the original raw image feature space. Query-adaptive weights are then rapidly computed by evaluating the proximity between a query and the concept categories. With the adaptive bit weights, the returned images can be ordered by weighted Hamming distance at a finer-grained binary code level rather than at the original integer Hamming distance level. Experimental results on a Flickr image dataset show clear improvements from our query-adaptive ranking approach.