Deletion Algorithm Research Articles

Proper Interval Vertex Deletion

The NP-complete problem Proper Interval Vertex Deletion is to decide whether an input graph on n vertices and m edges can be turned into a proper interval graph by deleting at most k vertices. Van Bevern et al. (In: Proceedings WG 2010. Lecture notes in computer science, vol. 6410, pp. 232---243, 2010) showed that this problem can be solved in $\mathcal {O}((14k +14)^{k+1} kn^{6})$ time. We improve this result by presenting an $\mathcal {O}(6^{k} kn^{6})$ time algorithm for Proper Interval Vertex Deletion. Our fixed-parameter algorithm is based on a new structural result stating that every connected component of a {claw,net,tent,C4,C5,C6}-free graph is a proper circular arc graph, combined with a simple greedy algorithm that solves Proper Interval Vertex Deletion on {claw,net,tent,C4,C5,C6}-free graphs in $\mathcal {O}(n+m)$ time. Our approach also yields a polynomial-time 6-approximation algorithm for the optimization variant of Proper Interval Vertex Deletion.

유효시간 데이터 스트림에서의 스카이라인 질의 알고리즘

Abstract Multi-criteria result extraction is crucial in many scientific applications that support real-time stream processing, such as habitat research and disaster monitoring. Skyline evaluation is computational intensive especially over continuous time-interval data streams where each object has its own customized expiration time. In this work, we propose TI-Sky – a continuous skyline evaluation framework. To ensure correctness, the result space needs to be continuously maintained as new objects arrive and older objects expire. TI-Sky strikes a perfect balance between the costs of continuously maintaining the result space and the costs of computing the final skyline result from this space whenever a pull-based user query is received. Our key principle is to incrementally maintain a partially precomputed skyline result space – however doing so efficiently by working at a higher level of abstraction. TI-Sky’s algorithms for insertion, deletion, purging and result retrieval exploit both layers of granularity. Our experimental study demonstrates the superiority of TI-Sky over existing techniques to handle a wide variety of data sets.

A LEMPEL-ZIV COMPLEXITY-BASED NEURAL NETWORK PRUNING ALGORITHM

This paper presents a pruning method for artificial neural networks (ANNs) based on the 'Lempel-Ziv complexity' (LZC) measure. We call this method the 'silent pruning algorithm' (SPA). The term 'silent' is used in the sense that SPA prunes ANNs without causing much disturbance during the network training. SPA prunes hidden units during the training process according to their ranks computed from LZC. LZC extracts the number of unique patterns in a time sequence obtained from the output of a hidden unit and a smaller value of LZC indicates higher redundancy of a hidden unit. SPA has a great resemblance to biological brains since it encourages higher complexity during the training process. SPA is similar to, yet different from, existing pruning algorithms. The algorithm has been tested on a number of challenging benchmark problems in machine learning, including cancer, diabetes, heart, card, iris, glass, thyroid, and hepatitis problems. We compared SPA with other pruning algorithms and we found that SPA is better than the 'random deletion algorithm' (RDA) which prunes hidden units randomly. Our experimental results show that SPA can simplify ANNs with good generalization ability.

Approximation and Tidying—A Problem Kernel for s-Plex Cluster Vertex Deletion

We introduce the s-Plex Cluster Vertex Deletion problem. Like the Cluster Vertex Deletion problem, it is NP-hard and motivated by graph-based data clustering. While the task in Cluster Vertex Deletion is to delete vertices from a graph so that its connected components become cliques, the task in s-Plex Cluster Vertex Deletion is to delete vertices from a graph so that its connected components become s-plexes. An s-plex is a graph in which every vertex is nonadjacent to at most s-1 other vertices; a clique is an 1-plex. In contrast to Cluster Vertex Deletion, s-Plex Cluster Vertex Deletion allows to balance the number of vertex deletions against the sizes and the density of the resulting clusters, which are s-plexes instead of cliques. The focus of this work is the development of provably efficient and effective data reduction rules for s-Plex Cluster Vertex Deletion. In terms of fixed-parameter algorithmics, these yield a so-called problem kernel. A similar problem, s-Plex Editing, where the task is the insertion or the deletion of edges so that the connected components of a graph become s-plexes, has also been studied in terms of fixed-parameter algorithmics. Using the number of allowed graph modifications as parameter, we expect typical parameter values for s-Plex Cluster Vertex Deletion to be significantly lower than for s-Plex Editing, because one vertex deletion can lead to a high number of edge deletions. This holds out the prospect for faster fixed-parameter algorithms for s-Plex Cluster Vertex Deletion.

Mechanism of User Profile Complete Deletion Concerning Temporary Scenario Oriented Application of Mobile SNS

In order to ensure the privacy of user profile from disclosure when the users quit using the mobile social network service (MSNS) at temporary scenarios, the paper proposes the privacy insurance module (PIM) based on distributed mobile social network service (DMSNS), which supports triggering the user profile complete deletion on several conditions. One of the conditions the paper proposes is the customized time setting for user profile deletion and the paper also designs the mechanism and algorithms for proper complete deletion by classification, which enriches the user experience and meanwhile protects user profile from being misused and disclosed.

An index-split Bloom filter for deep packet inspection

Deep packet inspection (DPI) scans both packet headers and payloads to search for predefined signatures. As link rates and traffic volumes of Internet are constantly growing, DPI is facing the high performance challenge of how to achieve line-speed packet processing with limited embedded memory. The recent trie bitmap content analyzer (TriBiCa) suffers from high update overhead and many false positive memory accesses, while the shared-node fast hash table (SFHT) suffers from high update overhead and large memory requirements. This paper presents an index-split Bloom filter (ISBF) to overcome these issues. Given a set of off-chip items, an index of each item is split apart into several groups of constant bits, and each group of bits uses an array of on-chip parallel counting Bloom filters (CBFs) to represent the overall off-chip items. When an item is queried, several groups of on-chip parallel CBFs constitute an index of an off-chip item candidate for a match. Furthermore, we propose a lazy deletion algorithm and vacant insertion algorithm to reduce the update overhead of ISBF, where an on-chip deletion bitmap is used to update on-chip parallel CBFs, not adjusting other related off-chip items. The ISBF is a time/space-efficient data structure, which not only achieves O(1) average memory accesses of insertion, deletion, and query, but also reduces the memory requirements. Experimental results demonstrate that compared with the TriBiCa and SFHT, the ISBF significantly reduces the off-chip memory accesses and processing time of primitive operations, as well as both the on-chip and off-chip memory sizes.

Random binary search tree with equal elements

We consider random binary search trees when the input consists of a multiset, i.e. a set with multiple occurrences of equal elements, and prove that the randomized insertion and deletion algorithms given by Martínez and Roura (1998) [4] produce random search trees regardless of multiplicities; even if all the elements are equal during the tree updates, a search tree will maintain its randomness. Thus, equal elements do not degenerate a random search tree and they need not to be handled in any special way. We consider also stability of a search tree with respect to its inorder traversal and prove that the algorithms used produce stable trees. This implies an implicit indexing of equal elements giving another proof that multiplicities do not pose problems when maintaining random binary search trees.

A “Nano-Dial” Molecular Computing Model Based on Circular DNA

A novel molecular computing model based on circular DNA was developed to solve a 3-coloring graph problem. This computing model uses circular DNA and works as to dial a number. The method of selecting true solutions is similar to dialing on a telephone. Moreover, the key methods in this model were circularization of single single-strand DNA (ssDNA) molecules and a backtracking deletion algorithm. In the course of computing, the structure of the DNA molecule was transformed into linear double-strand DNA (dsDNA), linear ssDNA, and circular ssDNA. For a 3-coloring graph problem with n vertices, the algorithm time complexity and the space complexity are both O(n2) at most. The computing achievement by this model indicates that circular DNA has extensive applications in molecular computing research. Keywords: Circular DNA, backtracking, algorithm complexity, 3-coloring graph problem

A gas-phase electron diffraction and quantum chemical investigation of the molecular structure of 1-bromosilacyclobutane

The gas-phase electron diffraction experiment has shown that 1-monobromosilacyclobutane (MBSCB) exists in two conformational forms, the axial and equatorial with a significantly higher prevalence of the latter form (73(6)%). Various quantum mechanical procedures have been applied to investigate the thermodynamic equilibrium of the two conformers as well as the geometrical parameters of MBSCB. Among these methods was MP2/6-311++G(2df,2pd). This level of theory provided an axial to equatorial ratio of 29:71% and values for the geometrical parameters that are in good agreement with the experimental values except for the C–C bond length, which is by 0.02 Å shorter than in the experiment. The main geometrical parameters obtained from the experiment are: ( r a Å, ∠ a°): Si–C 1.872(3); C–C 1.583(6); Si–Br 2.225(3); ∠ CSiC 79.3; dihedral angle φ 28.8(52) ( axial) and 39.9(2) ( equatorial). Natural bond orbital (NBO) and atoms in molecule (AIM) analyses have been performed. Both, the donor–acceptor (Lewis and non-Lewis) orbital interactions and the topological properties of the charge density at the critical points ρ( r) have consistently confirmed the experimental results and facilitated their interpretation. For the purpose of comparison and systematic investigation, we optimized the geometries and analyzed the NBOs and the topological properties of silacyclobutane, 1-monofluorosilacyclobutane (MFSCB), and 1-monochlorosilacyclobutane (MCSCB). Simple relationship has been found between the puckering angle θ and the puckering amplitude q, which allows for the prediction of either θ or q for mono- and dihaloginated silacyclobutanes. Additionally, NBO deletion analysis comprising NOSTAR, NOVIC, and NOGEM deletion algorithms have been conducted. Interesting conclusions regarding structure and conformational stability of the studied monohalogenated silacyclobutanes could be drawn from this analysis.

The molecular structure of 1,1-dichlorosilacyclopentane as obtained from gas-phase electron diffraction and ab initio calculations

The molecular structure of 1,1-dichlorosilacyclopentane (DCSCP) has been investigated by means of gas-phase electron diffraction and quantum mechanical calculation. We applied both a pseudorotation model to account for the dynamic and large amplitude motion in DCSCP, and a one-conformer model of C 1 symmetry. Using the computational results we analyzed the dependency of the ring geometrical parameters and vibrational mean amplitudes on the phase angle φ. The joint electron diffraction and ab initio study has led to the following r a structural parameters of DCSCP ( C 1 conformer): r(Si–Cl) = 2.047(2) Å, r(Si–C) = 1.867(4) Å, average r(C–C) ring = 1.548(4) Å, average r(C–H) = 1.103(7) Å, <(C–Si–C) = 97.4(6)°, <(Cl–Si–Cl) = 104.8(10)°, and effective phase angle φ = 74.8(58)°. The puckering amplitude for the five-membered ring was determined to be q = 0.480(24) Å. The quantum mechanical calculations were performed by utilizing the UHF, B3LYP, and MP2 methods in combination with basis sets 6-311++G(2df,2pd), 6-311++G(df,pd), 6-311++G(p,d), 6-311+G(d,p), 6-311G(d,p) and Dunning double and triple zeta (with and without augmentation). All these methods have consistently shown that the C 2 conformer is more stable than the C s symmetric form. For all calculations we used the MOLPRO and Gaussian03 packages. NBO and AIM analyses were also carried out to explore the bond/anti-bond hyperconjugative interactions and the topological properties of the charge density distribution in DCSCP. NBO scheme including second-order perturbation analysis has shown that the major orbital stabilizing interactions are between the chlorine lone pair ( n π) Cl and the low-lying σ Si – C2 ∗ and σ Si – C5 ∗ antibonding orbitals. It was found that remote σ Si–C → σ C – H ∗ interactions are stabilized by 4.4 kcal mol −1 and contribute to the stabilization of the C 2 conformer in DCSCP. Deletion analysis was performed using various deletion algorithms like NOSTAR, NOVIC, NOGEM (see text). The stabilization energy for the C 2 conformer resulting from the difference of the non-Lewis energy E(NL) C 2 – E(NL) Cs was 7.1 kcal mol −1. Similar analyses using the same quantum mechanical procedures mentioned above have been conducted to study silacyclopentane (SCP), 1,1-difluorosilacyclopentane (DFSCP), and 1,1-dibromosilacyclopentane (DBSCP).

DELETING A MARKED BASIS-STATE FROM AN EVEN SUPERPOSITION OF ALL BASIS-STATES WITH A SINGLE QUERY

We present a quantum deletion algorithm that deletes a marked basis-state from an even superposition of all N basis-states. This algorithm uses only a single query and achieves exponential speed-up compared with classical analog where Θ(N) queries are required.

Maintenance of fast updated frequent pattern trees for record deletion

The Frequent-Pattern-tree (FP tree) is an efficient data structure for association-rule mining without generation of candidate itemsets. It was used to represent a database into a tree structure which stored only frequent items. It, however, needed to process all transactions in a batch way. In the past, Hong et al. thus proposed an efficient incremental mining algorithm for handling newly inserted transactions. In addition to record insertion, record deletion from databases is also commonly seen in real-applications. In this paper, we thus attempt to modify the FP-tree construction algorithm for efficiently handling deletion of records. A fast updated FP-tree (FUFP-tree) structure is used, which makes the tree update process become easier. An FUFP-tree maintenance algorithm for the deletion of records is also proposed for reducing the execution time in reconstructing the tree when records are deleted. Experimental results also show that the proposed FUFP-tree maintenance algorithm for deletion of records runs faster than the batch FP-tree construction algorithm for handling deleted records and generates nearly the same tree structure as the FP-tree algorithm. The proposed approach can thus achieve a good trade-off between execution time and tree complexity.

Randomness Preserving Deletions on Special Binary Search Trees

Deletions in binary search trees are difficult to analyse as they are not randomness preserving. We will present a new kind of tree which differs slightly from the standard binary search tree. It will be referred to as an ordered binary search tree as it stores a history element in its nodes, which provides information about the order in which the nodes were inserted. Using this extra information it is possible to design a new randomness preserving and order preserving deletion algorithm.

Integral ear elimination and virtual point-based updating algorithms for constrained Delaunay TIN

Constrained Delaunay Triangular Irregular Networks (CD-TIN), a kind of special data structure, have many practical applications in Geoinformatics, especially in the representation of linear constrained triangulation for DTM and DSM, such as in digital city and digital mine. Past researches on D-TIN mainly focused on point insertion and deletion without consideration of constraint, and that on CD-TIN usually paid more attention to the insertion algorithms for points and edges, but little to the deletion algorithms. The presented algorithms are far insufficient for the dynamic updating of CD-TIN. In this paper, the constraint edge in CD-TIN is considered to be any set of broken lines, i.e., polygon edges, broken lines and simple segments. The constraint edge may be composed of one or more constraint segments, and it is allowed to be in any form: Open or close, intersection or self-intersection. By improving to present insertion and deletion algorithms for D-TIN, two new algorithms for CD-TIN updating are presented. According to the polymorphism of the constraints in CD-TIN, virtual point is adopted to represent the crossing node between constraint edges when a constraint edge is inserted in CD-TIN. Two new algorithms named as Integral Ear Elimination (IEE) and Influence Domain Retriangulation for Virtual Point (IDRVP) are presented, the former is for constraint point deletion, while the later is for the insertion and deletion of constraint edge. The principle of IDRVP is that to divide the influence domain of a virtual point into some parts by the constraint-keeping edges, and to retriangulate each part of the influence domain individually referring to the constraint visible property and constraint empty circle (CEC) criterion. Finally, a prototype system is developed with VC++, one case on the integration of 3D terrain and buildings is demonstrated to test the correctness of new algorithms. It shows that the new algorithms are effective for the updating of CD-TIN.

Reliability improvement for an RFID-based psychiatric patient localization system

Collaboration between Field Generators, Readers and Tags generates the required functions in using radio frequency identification (RFID) for psychiatric patient localization. The Field Generator continually transmits trigger signals within its transmission range. When a Tag, which a patient wears, receives a trigger signal from a Field Generator, the Tag responds to a Reader with its own ID and ID of the Field Generator that issues the trigger. Based on Field Generator IDs that a Tag responds to, the location of the patient wearing the Tag can be estimated approximately. However, in recent RFID based localization systems, certain phenomena impact the reliability of signal transmission and decrease the feasibility of the localization system. To eliminate interference from different Field Generators, this study presents a novel graph coloring with merging and deletion (GCMD) algorithm for such a localization system that eliminates interference from Field Generators located near each other. Experimental results indicate that the GCMD algorithm significantly improves localization system reliability, thereby increasing the feasibility of RFID for psychiatric patient localization.

A generalized direct‐particle‐deletion scheme for the calculation of chemical potential and solubilities of small‐ and medium‐sized molecules in amorphous polymers

The development, validation, and first applications of a generalized version of an inverse Widom method are described. It permits the calculation of solubility coefficients for molecules as large as, e.g., benzene in all polymers for which reasonable forcefield parameters exist. Predicting the solubility is a key to the knowledge-based design of materials utilized to solve permeability related problems. For long time, particle insertion methods, such as the Widom method, were the only way to predict solubilities from molecular models, but they, in most cases, only worked well for rather small penetrants (e.g., H2, O2, N2). Therefore, a few years ago, a new particle deletion algorithm "DPD" was introduced by Boulougouris, Economou, and Theodorou to overcome this problem in principle. The related computer code was, however, only applicable to special, relatively simple model systems. As application examples for the generalized version described here, solubility calculations for nitrogen, oxygen, and benzene in poly(dimethyl siloxane) are presented.

A 2-Level TCAM Architecture for Ranges

As the demand for high-quality Internet increases, emerging network applications are spurring the need for faster, feature-rich, and cost-effective routers. Multifield packet classification in routers has been a computation-intensive data path function for software implementation. Therefore, solutions for packet classification based on hardware design, such as Ternary Content Addressable Memory (TCAM), are necessary to sustain gigabit line processing rate. Traditionally, TCAMs have been designed for storing prefixes. However, multifield packet classification usually involves two fields of arbitrary ranges that are TCP/IP layer 4 source and destination ports. Storing ranges in TCAMs relies on decomposing each individual range into multiple prefixes, which leads to range-to-prefix blowout. To reduce the total number of prefixes needed to represent all ranges, this paper proposes a 2-level TCAM architecture and two range-to-prefix conversion schemes. In the first proposed scheme, designed for disjoint ranges, the maximum number of entries needed in TCAM is 2m-1 for m disjoint ranges. In the second proposed scheme, designed for contiguous ranges, only m TCAM entries are needed. In a general case of n arbitrary ranges, all ranges can first be converted into disjoint ranges or contiguous ranges and then the proposed algorithms can be applied. As a result, only 4n-3 TCAM entries are needed for the disjoint ranges and only 2n+1 TCAM entries are needed for contiguous ranges. This paper also proposes insertion and deletion algorithms to accommodate incremental changes to the range sets. The experiments made show that the proposed range-to-prefix conversion schemes perform better than the existing schemes in terms of the number of required TCAM entries and execution time for range update operations.

Theoretical Convergence Analysis of a General Division–deletion Algorithm for Solving Global Search Problems

Presented in this paper is the prototype of a very general algorithm referred to as Division --- Deletion Algorithm (DDA) for solving the most general global search problem. Various necessary conditions, sufficient conditions, and necessary and sufficient conditions for the convergence of the algorithm are proposed and analyzed. As an example of its application, we demonstrate that the convergence of a standard Hansen's interval algorithm for unconstrained global optimization simply follows from this general theory.

Application of Simulated Annealing to the Biclustering of Gene Expression Data

In a gene expression data matrix, a bicluster is a submatrix of genes and conditions that exhibits a high correlation of expression activity across both rows and columns. The problem of locating the most significant bicluster has been shown to be NP-complete. Heuristic approaches such as Cheng and Church's greedy node deletion algorithm have been previously employed. It is to be expected that stochastic search techniques such as evolutionary algorithms or simulated annealing might improve upon such greedy techniques. In this paper we show that an approach based on simulated annealing is well suited to this problem, and we present a comparative evaluation of simulated annealing and node deletion on a variety of datasets. We show that simulated annealing discovers more significant biclusters in many cases. Furthermore, we also test the ability of our technique to locate biologically verifiable biclusters within an annotated set of genes.

Infeasibility in Automated Test Assembly Models: A Comparison Study of Different Methods

Several techniques exist to automatically put together a test meeting a number of specifications. In an item bank, the items are stored with their characteristics. A test is constructed by selecting a set of items that fulfills the specifications set by the test assembler. Test assembly problems are often formulated in terms of a model consisting of restrictions and an objective to be maximized or minimized. A problem arises when it is impossible to construct a test from the item pool that meets all specifications, that is, when the model is not feasible. Several methods exist to handle these infeasibility problems. In this article, test assembly models resulting from two practical testing programs were reconstructed to be infeasible. These models were analyzed using methods that forced a solution (Goal Programming, Multiple‐Goal Programming, Greedy Heuristic), that analyzed the causes (Relaxed and Ordered Deletion Algorithm (RODA), Integer Randomized Deletion Algorithm (IRDA), Set Covering (SC), and Item Sampling), or that analyzed the causes and used this information to force a solution (Irreducible Infeasible Set‐Solver). Specialized methods such as the IRDA and the Irreducible Infeasible Set‐Solver performed best. Recommendations about the use of different methods are given.