Previous Best-known Algorithm Research Articles

A New Algorithm for Fast Generalized DFTs

We give an new arithmetic algorithm to compute the generalized Discrete Fourier Transform (DFT) over finite groups G . The new algorithm uses O (∣ G ∣ ω /2 + o (1) ) operations to compute the generalized DFT over finite groups of Lie type, including the linear, orthogonal, and symplectic families and their variants, as well as all finite simple groups of Lie type. Here ω is the exponent of matrix multiplication, so the exponent ω/2 is optimal if ω = 2. Previously, “exponent one” algorithms were known for supersolvable groups and the symmetric and alternating groups. No exponent one algorithms were known, even under the assumption ω = 2, for families of linear groups of fixed dimension, and indeed the previous best-known algorithm for SL 2 (F q ) had exponent 4/3 despite being the focus of significant effort. We unconditionally achieve exponent at most 1.19 for this group and exponent one if ω = 2. Our algorithm also yields an improved exponent for computing the generalized DFT over general finite groups G , which beats the longstanding previous best upper bound for any ω. In particular, assuming ω = 2, we achieve exponent √ 2, while the previous best was 3/2.

Efficient Record Linkage Algorithms Using Complete Linkage Clustering.

Data from different agencies share data of the same individuals. Linking these datasets to identify all the records belonging to the same individuals is a crucial and challenging problem, especially given the large volumes of data. A large number of available algorithms for record linkage are prone to either time inefficiency or low-accuracy in finding matches and non-matches among the records. In this paper we propose efficient as well as reliable sequential and parallel algorithms for the record linkage problem employing hierarchical clustering methods. We employ complete linkage hierarchical clustering algorithms to address this problem. In addition to hierarchical clustering, we also use two other techniques: elimination of duplicate records and blocking. Our algorithms use sorting as a sub-routine to identify identical copies of records. We have tested our algorithms on datasets with millions of synthetic records. Experimental results show that our algorithms achieve nearly 100% accuracy. Parallel implementations achieve almost linear speedups. Time complexities of these algorithms do not exceed those of previous best-known algorithms. Our proposed algorithms outperform previous best-known algorithms in terms of accuracy consuming reasonable run times.

A splicing-driven memetic algorithm for reconstructing cross-cut shredded text documents

Reconstruction of cross-cut shredded text documents (RCCSTD) plays a crucial role in many fields such as forensic and archeology. To handle and reconstruct the shreds, in addition to some image processing procedures, a well-designed optimization algorithm is required. Existing works adopt some general methods in these two aspects, which may not be very efficient since they ignore the specific structure or characteristics of RCCSTD. In this paper, we develop a splicing-driven memetic algorithm (SD-MA) specifically for tackling the problem. As the name indicates, the algorithm is designed from a splicing-centered perspective, in which the operators and fitness evaluation are developed for the purpose of splicing the shreds. We design novel crossover and mutation operators that utilize the adjacency information in the shreds to breed high-quality offsprings. Then, a local search strategy based on shreds is performed, which further improves the evolution efficiency of the population in complex search space. To extract valid information from shreds and improve the accuracy of splicing costs, we propose a comprehensive objective function that considers both edge and empty row-based splicing errors. Experiments are carried out on 30 RCCSTD scenarios and comparisons are made against previous best-known algorithms. Experimental results show that the proposed SD-MA displays a significantly improved performance in terms of solution accuracy and convergence speed.

RLT-S: A Web System for Record Linkage.

BackgroundRecord linkage integrates records across multiple related data sources identifying duplicates and accounting for possible errors. Real life applications require efficient algorithms to merge these voluminous data sources to find out all records belonging to same individuals. Our recently devised highly efficient record linkage algorithms provide best-known solutions to this challenging problem.MethodWe have developed RLT-S, a freely available web tool, which implements our single linkage clustering algorithm for record linkage. This tool requires input data sets and a small set of configuration settings about these files to work efficiently. RLT-S employs exact match clustering, blocking on a specified attribute and single linkage based hierarchical clustering among these blocks.ResultsRLT-S is an implementation package of our sequential record linkage algorithm. It outperforms previous best-known implementations by a large margin. The tool is at least two times faster for any dataset than the previous best-known tools.ConclusionsRLT-S tool implements our record linkage algorithm that outperforms previous best-known algorithms in this area. This website also contains necessary information such as instructions, submission history, feedback, publications and some other sections to facilitate the usage of the tool.AvailabilityRLT-S is integrated into http://www.rlatools.com, which is currently serving this tool only. The tool is freely available and can be used without login. All data files used in this paper have been stored in https://github.com/abdullah009/DataRLATools. For copies of the relevant programs please see https://github.com/abdullah009/RLATools.

Efficient sequential and parallel algorithms for record linkage

Background and objectiveIntegrating data from multiple sources is a crucial and challenging problem. Even though there exist numerous algorithms for record linkage or deduplication, they suffer from either large time needs or restrictions on the number of datasets that they can integrate. In this paper we report efficient sequential and parallel algorithms for record linkage which handle any number of datasets and outperform previous algorithms.MethodsOur algorithms employ hierarchical clustering algorithms as the basis. A key idea that we use is radix sorting on certain attributes to eliminate identical records before any further processing. Another novel idea is to form a graph that links similar records and find the connected components.ResultsOur sequential and parallel algorithms have been tested on a real dataset of 1 083 878 records and synthetic datasets ranging in size from 50 000 to 9 000 000 records. Our sequential algorithm runs at least two times faster, for any dataset, than the previous best-known algorithm, the two-phase algorithm using faster computation of the edit distance (TPA (FCED)). The speedups obtained by our parallel algorithm are almost linear. For example, we get a speedup of 7.5 with 8 cores (residing in a single node), 14.1 with 16 cores (residing in two nodes), and 26.4 with 32 cores (residing in four nodes).ConclusionsWe have compared the performance of our sequential algorithm with TPA (FCED) and found that our algorithm outperforms the previous one. The accuracy is the same as that of this previous best-known algorithm.

A Branch, Bound, and Remember Algorithm for the Simple Assembly Line Balancing Problem

We present a new exact algorithm for the assembly line balancing problem. The algorithm finds and verifies the optimal solution for every problem in the combined benchmarks of Hoffmann, Talbot, and Scholl in less than one-half second per problem, on average, including one problem that has remained open for over 10 years. The previous best-known algorithm is able to solve 257 of the 269 benchmarks. The new algorithm is based on a branch-and-bound method that uses memory to eliminate redundant subproblems.

Routing with multiple quality-of-services constraints: An approximation perspective

Finding a path that satisfies multiple Quality-of-Service (QoS) constraints is vital to the deployment of current emerged services. However, existing algorithms are not very efficient and effective at finding such a path. Moreover, few works focus on three or more QoS constraints. In this paper, we present an enhanced version of fully polynomial time approximation scheme (EFPTAS) for multiconstrainted path optimal (MCOP) problem. Specifically, we make four major contributions. We first allow the proposed algorithm to construct an auxiliary graph, through which the QoS parameters on each of the finding path can be guaranteed not to exceed the given constraints. Then we adopt a concept, called nonlinear definition of path constraints in EFPTAS for reducing both time and space complexity. Also, we enable EFPTAS to run iteratively to facilitate a progressive refinement of the finding result. In addition to these, we identify some “deployment” issues for proposed algorithm, the essential steps that how and when the EFPTAS takes place are presented. By analyzing the proposed algorithm theoretically, we find that the presented EFPTAS can find a ( 1 + ε )-approximation path in the network with time complexity O ( | E | | V | / ε ) (where | E | is the number of edges and | V | is the number of nodes), which outperforms the previous best-known algorithm for MCOP. We conduct an extensive comparison between the algorithm presented in this paper and previous best-known study experimentally, our results indicate that EFPTAS can find a path with low complexity and preferable quality.

Deferred‐query: An efficient approach for some problems on interval graphs

This paper introduces the idea of a deferred-query approach to design O(n) algorithms for the domatic partition, optimal path cover, Hamiltonian path, Hamiltonian circuit, and maximum matching problems on interval graphs given n endpoint-sorted intervals. The previous best-known algorithms run in O(n log log n) or O(n +m) time, where m is the number of edges in the corresponding interval graphs. © 1999 John Wiley & Sons, Inc. Networks 34: 1–10, 1999

Deferred-query: An efficient approach for some problems on interval graphs

This paper introduces the idea of a deferred-query approach to design O(n) algorithms for the domatic partition, optimal path cover, Hamiltonian path, Hamiltonian circuit, and maximum matching problems on interval graphs given n endpoint-sorted intervals. The previous best-known algorithms run in O(n log log n) or O(n + m) time, where m is the number of edges in the corresponding interval graphs.

A new technique to compute polygonal schema for 2-manifolds with application to null-homotopy detection

We provide a new technique for deriving optimal-sized polygonal schema for triangulated compact 2-manifolds without boundary inO(n) time, wheren is the size of the given triangulationT. We first derive a polygonal schemaP embedded inT using Seifert-Van Kampen's theorem. A reduced polygonal schemaQ of optimal size is computed fromP, where a surjective map from the vertices ofP is retained to the vertices ofQ. This helps detecting null-homotopic (contractible to a point) cycles. Given a cycle of lengthk, we determine if it is null-homotopic inO(n+k logg) time and in θ(n+k) space, whereg is the genus of the given 2-manifold. The actual contraction for a null-homotopic cycle can be computed in θ(nk) time and space. This is a considerable improvement over the previous best-known algorithm for this problem.

An efficient parallel algorithm for the single function coarsest partition problem

We describe an efficient parallel algorithm to solve the single function coarsest partition problem. The algorithm runs in O (log n) time using O( n log log n) operations on the arbitrary CRCW PRAM. The previous best-known algorithms run in O(log 2 n) time using O( n log 2 n) operations on the CREW PRAM, and O(log n) time using O ( n log n) operations on the arbitrary CRCW PRAM. Our solution is based on efficient algorithms for solving several subproblems that are of independent interest. In particular, we present efficient parallel algorithms to find a minimal starting point of a circular string with respect to lexicographic ordering and to sort lexicographically a list of strings of different lengths.