Approximate Matching Problem Research Articles

Q-gram matching using tree models

q-gram matching is used for approximate substring matching problems in a wide range of application areas, including intrusion detection. In this paper, we present a tree-based model to perform fast linear time q-gram matching. All q-grams present in the text are stored in a tree structure similar to trie. We use a tree redundancy pruning algorithm to reduce the size of the tree without losing any information. We also use suffix links for fast q-gram search during query matching. We compare our work with the Rabin-Karp-based hash-table technique, commonly used for multiple q-gram search. We present results of experiments on system call sequence data used for intrusion detection.

Simple algorithms for partial point set pattern matching under rigid motion

This paper presents simple and deterministic algorithms for partial point set pattern matching in 2D. Given a set P of n points, called sample set, and a query set Q of k points ( n ⩾ k ), the problem is to find a matching of Q with a subset of P under rigid motion. The match may be of two types: exact and approximate. If an exact matching exists, then each point in Q coincides with the corresponding point in P under some translation and/or rotation. For an approximate match, some translation and/or rotation may be allowed such that each point in Q lies in a predefined ε -neighborhood region around some point in P. The proposed algorithm for the exact matching needs O ( n 2 ) space and O ( n 2 log n ) preprocessing time. The existence of a match for a given query set Q can be checked in O ( k α log n ) time in the worst-case, where α is the maximum number of equidistant pairs of point in P. For a set of n points, α may be O ( n 4 / 3 ) in the worst-case. Some applications of the partial point set pattern matching are then illustrated. Experimental results on random point sets and some fingerprint databases show that, in practice, the computation time is much smaller than the worst-case requirement. The algorithm is then extended for checking the exact match of a set of k line segments in the query set with a k-subset of n line segments in the sample set under rigid motion in O ( kn log n ) time. Next, a simple version of the approximate matching problem is studied where one point of Q exactly matches with a point of P, and each of the other points of Q lie in the ε -neighborhood of some point of P. The worst-case time and space complexities of the proposed algorithm are O ( n 2 k 2 log n ) and O ( n ) , respectively. The proposed algorithms will find many applications to fingerprint matching, image registration, and object recognition.

Exact and approximate graph matching using random walks

In this paper, we propose a general framework for graph matching which is suitable for different problems of pattern recognition. The pattern representation we assume is at the same time highly structured, like for classic syntactic and structural approaches, and of subsymbolic nature with real-valued features, like for connectionist and statistic approaches. We show that random walk based models, inspired by Google's PageRank, give rise to a spectral theory that nicely enhances the graph topological features at node level. As a straightforward consequence, we derive a polynomial algorithm for the classic graph isomorphism problem, under the restriction of dealing with Markovian spectrally distinguishable graphs (MSD), a class of graphs that does not seem to be easily reducible to others proposed in the literature. The experimental results that we found on different test-beds of the TC-15 graph database show that the defined MSD class "almost always" covers the database, and that the proposed algorithm is significantly more efficient than top scoring VF algorithm on the same data. Most interestingly, the proposed approach is very well-suited for dealing with partial and approximate graph matching problems, derived for instance from image retrieval tasks. We consider the objects of the COIL-100 visual collection and provide a graph-based representation, whose node's labels contain appropriate visual features. We show that the adoption of classic bipartite graph matching algorithms offers a straightforward generalization of the algorithm given for graph isomorphism and, finally, we report very promising experimental results on the COIL-100 visual collection.

Approximate Matching of Run-Length Compressed Strings

We focus on the problem of approximate matching of strings that have been compressed using run-length encoding. Previous studies have concentrated on the problem of computing the longest common subsequence (LCS) between two strings of length m and n , compressed to m' and n' runs. We extend an existing algorithm for the LCS to the Levenshtein distance achieving O(m'n+n'm) complexity. Furthermore, we extend this algorithm to a weighted edit distance model, where the weights of the three basic edit operations can be chosen arbitrarily. This approach also gives an algorithm for approximate searching of a pattern of m letters (m' runs) in a text of n letters (n' runs) in O(mm'n') time. Then we propose improvements for a greedy algorithm for the LCS, and conjecture that the improved algorithm has O(m'n') expected case complexity. Experimental results are provided to support the conjecture.

Exact and approximate matching of matrix languages

In this paper we consider the problem of exact and approximate matching of matrix languages. In the exact image testing problem, we have given polynomial time algorithms for the membership problem for matrix grammars. We then consider the problem of approximately matching matrix languages. Given a matrix grammar M, a cost function and an input image I, we give algorithms to approximately match the input image with images generated by the grammar. The algorithms return the cost of matching the input image with an image generated by the matrix grammar. These approximation schemes can be used for pattern recognition.

Reversing the Error-Correction Scheme for a Fault-Tolerant Indexing

Summary form only given. The article presents an innovative approach to approximate matching of multi-attribute objects based on reversing the conventional scheme of error-correction coding. The approximate matching problem primarily arises in information retrieval systems, which can store fuzzily described items and operate with nebulous searching criteria. To establish an approximate equivalence relation on a set of multi-attribute objects it has been suggested to apply a decoding procedure to binary vectors corresponding to these objects and to use the obtained message words as hash codes. With this hashing technique it is possible to construct fault-tolerant indices allowing certain mismatches of binary vectors in terms of Hamming metrics. The simplest practical realization of this technique is based on the so-called perfect Golay code which maps 23-bit vectors into 12-bit message words. In this case, two different 23-bit vectors at a Hamming distance of 2 would have some common 12-bit indices. This provides an organization of a direct retrieval of a neighborhood of 23 bit-vectors with up to two mismatches from a given key. The proposed technique employs a reasonable redundancy and can trade utilization of extra memory for the speed and range of searching. Besides a direct application to information retrieval, the developed technique is also beneficial for complex computational procedures incorporating near-matching operations. A typical procedure of this kind is recovering of closed matches from vector-quantization tables.

On the relation between state feedback and full information regulators in nonlinear singular H/sub ∞/ control

In this paper the relationship between state feedback control laws and full information control laws, i.e. control laws which make explicit use of the disturbance signals, is discussed in the framework of nonlinear singular H/sub /spl infin// control. In particular, it is shown that any (polynomial) full information control law can always be approximated by a state feedback control law, provided that a certain (arbitrarily small) amount of performance is sacrificed. Moreover, the obtained result is used to give alternative proofs and generalizations to some existing results in the area of global disturbance attenuation for nonlinear systems and to establish some new and interesting results regarding the problem of approximate model matching.

A constrained edit distance between unordered labeled trees

This paper considers the problem of computing a constrained edit distance between unordered labeled trees. The problem of approximate unordered tree matching is also considered. We present dynamic programming algorithms solving these problems in sequential timeO(|T1|×|T2|×(deg(T1)+deg(T2))× log2(deg(T1)+deg(T2))). Our previous result shows that computing the edit distance between unordered labeled trees is NP-complete.

Algorithms for approximate graph matching

Labeled graphs are graphs in which each node and edge has a label. The distance between two labeled graphs is considered to be the weighted sum of the costs of edit operations (insert, delete, and relabel the nodes and edges) to transform one graph to the other. The paper considers two variants of the approximate graph matching problem (AGM): Given a pattern graph P and a data graph D: 1. 1. What is the distance between P and D? 2. 2. What is the minimum distance between P and D when subgraphs can be freely removed from D? We first show that no efficient algorithm can solve either variant of the AGM unless P = NP. Then we present several heuristic algorithms leading to approximate solutions. The heuristics are based on probabilistic hill climbing and maximum flow techniques. Our experimental results involving the comparison of real and simulated data demonstrate the good performance of the algorithms presented.

Approximate Matching of Nonlinear Systems via Nonlinear H∞ methods

Abstract Based on some recent results on the problem of disturbance attenuation in nonlinear systems via the nonlinear analogue of the H ∞ - approach, a “nonlinear approximate matching problem” is solved which consists in finding an output feedback controller which renders the input-output behavior of a system approximately equal to that of an arbitrarily chosen reference model. An output feedback controller is found which stabilizes the system and guarantees that the (truncated) L 2 norm of a combined penalty variable which includes the matching error and the control is γ-times smaller than the (truncated) L 2 norm of the input to the reference model.

Simple Fast Algorithms for the Editing Distance between Trees and Related Problems

Ordered labeled trees are trees in which the left-to-right order among siblings is significant. The distance between two ordered trees is considered to be the weighted number of edit operations (insert, delete, and modify) to transform one tree to another. The problem of approximate tree matching is also considered. Specifically, algorithms are designed to answer the following kinds of questions:1. What is the distance between two trees? 2. What is the minimum distance between $T_1 $ and $T_2 $ when zero or more subtrees can be removed from $T_2 $? 3. Let the pruning of a tree at node n mean removing all the descendants of node n. The analogous question for prunings as for subtrees is answered. A dynamic programming algorithm is presented to solve the three questions in sequential time $O(|T_1 | \times |T_2 | \times \min ({\textit{depth}}(T_1 ),{\textit{leaves}}(T_1 )) \times \min ({\textit{depth}}(T_2 ),{\textit{leaves}}(T_2 )))$ and space $O(|T_1 | \times |T_2 |)$ compared with $O(|T_1 | \times |T_2 | \times ({\textit{depth}}(T_1 ))^2 \times ({\textit{depth}}(T_2 ))^2 )$ for the best previous published algorithm due to Tai [J. Assoc. Comput. Mach., 26 (1979), pp, 422-433]. Further, the algorithm presented here can be parallelized to give time $O(|T_1 | \times |T_2 |)$.