Maximum Intersection Research Articles

Performance Comparison of MISP-based MANET Strong DAD Protocol

A broadcast operation is the fundamental transmission technique in mobile ad-hoc networks (MANETs). Because a broadcast operation can cause a broadcast storm, only selected forwarding nodes have the right to rebroadcast a broadcast message among the one-hop and two-hop neighboring nodes of a sender. This paper proposes the maximum intersection self-pruning (MISP) algorithm to minimize broadcasting redundancy. Herein, an example is given to help describe the main concept of MISP and upper bounds of forward node have been derived based on induction. A simulation conducted demonstrated that when conventional blind flooding (BF), self-pruning (SP), an optimized link state routing (OLSR) multipoint relay (MPR) set, and dominant pruning (DP), are replaced with the MISP in executing Strong duplicate address detection (DAD), the performances in terms of the energy consumption, upper bounds of the number of forward nodes, and message complexity have been improved. In addition, to evaluate the performance in reference to the link error probability, P e , an enhancement was achieved by computing a proposed retransmission limit, S, for error recovery based on this probability. Retransmission limit control is critical for efficient energy consumption of MANET nodes operating with limited portable energy where Strong DAD reacts differently to link errors based on the operational procedures.

MATHEMATICAL METHODS FOR DETERMINING THE FOOT POINT OF THE ARTERIAL PULSE WAVE AND EVALUATION OF PROPOSED METHODS

The evaluation of the arterial wall condition is most frequently based on such markers as arterial pulse wave velocity (PWV) and pulse transit time (PTT). To calculate these markers, it is necessary to determine the location of the foot of the arterial pulse wave (APW). This foot point is usually determined with the help of the second derivate maximum or tangent intersection foot-to-foot methods. This paper proposes two original methods for locating the APW foot point, namely: the bottom straight-line and forefront tangent intersection method and the APW foot polynomial approximation method. The main objective of this study is to compare the originally proposed methods with the tangent intersection and the second derivate maximum methods, with respect to error dispersion under different sound-to-noise ratios (SNR) and difference between the foot point of the APW without noise (APW reference value) and the foot point of the APW with a certain SNR. The analysis of the APW signal with additive noise reveals that the second derivate maximum method results in the widest error dispersion, whereas the tangent intersection method results in the greatest difference between the APW reference value and the foot point of the APW with additive noise. The least difference between the APW reference value and the foot point of the APW with additive noise, as well as the least error dispersion is achieved in the APW foot polynomial approximation method.

Network Traffic Control in Cyber-Transportation Systems Accounting for User-Level Fairness

This research identifies the advantage of connected vehicle environment in cyber-transportation systems (CTS) and proposes control strategies that can yield benefits from system and user perspectives. Particularly, the focus is to minimize the total stopped delay at signalized intersections for the entire trip of a user. Further, we define and assess the notion of fairness from the user perspective. We develop and implement a vehicle-to-infrastructure (V2I)-based signal controller within the framework of CTS. The test results from a network containing 15 signalized intersections show that the proposed fair queuing (FQ) algorithm performs better than the fixed control and real-time adaptive control in terms of both efficiency (system travel time) and fairness (minimizing the difference between maximum and mean intersection delay) across users.

Super-simple (5, 4)-GDDs of group type g u

In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Supersimple group divisible designs are useful in constructing other types of supersimple designs which can be applied to codes and designs. In this article, the existence of a super-simple (5, 4)-GDD of group type gu is investigated and it is shown that such a design exists if and only if u ⩾ 5, g(u − 2) ⩾ 12, and u(u − 1)g2 ≡ 0 (mod 5) with some possible exceptions.

Extracting Parking Lot Structures from Aerial Photographs

A new method for the automatic extraction of parking lot structures from an aerial orthophoto is proposed which has two major stages. Line features of a parking lot are first extracted by using a line extraction method with principle orientation constraints which offers a reliable basis for the extraction of parking lots structures by emphasizing on the extraction of accurate parking line information. The structure of the parking lots are then determined from the extracted parking lines through a maximum intersection orientation method, parameter-estimating procedure, and a self-adaptive growth method. A comparative experiment is shown and the result indicates that the proposed method can effectively extract parking lot structures with high correctness, high-quality completeness, and good geometric accuracy.

Sampling Strategies for 3D Partial Shape Matching and Retrieval Using Bag-of-Words Model

This paper investigates the feature sampling strategies for 3D partial shape retrieval using bag-of-words model. The SHREC 09’ parts query models [3] are tested for comparison. These parts models are obtained by cutting parts from complete models, which are different from range scans. Dense sampling and pyramid sampling are proposed to extract local salient features from the depth images of the 3D models. Bag-of-words model is used to represent of both of parts query and complete target models. The optimal sampling configurations for the proposed feature extraction strategies are obtained by comparing the retrieval accuracy using maximum histogram intersection distance (MHID). The results suggest that extracting more features does not guarantee better retrieval accuracy using the bag-of-words model. The feature sampling configurations also have significant impacts on the retrieval accuracy.

Synchronisation of systems with individual dynamics by static networked controllers

AbstractThe paper deals with the synchronisation of subsystems that have individual linear dynamics. To formulate the basic condition under which the subsystems can be synchronised, the notion of system intersection is introduced. Subsystems can be synchronised by an appropriate controller only if their dynamics have a non‐empty intersection, which acts as a virtual reference system. The paper describes an algorithm for determining the maximum intersection of linear systems and gives an explicit relation for the initial state in dependence upon the subsystem initial states, for which the virtual reference system generates the synchronous trajectory.

On the separability of graphs

Recently, Cicalese and Milanič introduced a graph-theoretic concept called separability. A graph is said to be k-separable if any two non-adjacent vertices can be separated by the removal of at most k vertices. The separability of a graph G is the least k for which G is k-separable. In this paper, we investigate this concept under the following three aspects.First, we characterize the graphs for which in any non-complete connected induced subgraph the connectivity equals the separability, so-called separability-perfect graphs. We list the minimal forbidden induced subgraphs of this condition and derive a complete description of the separability-perfect graphs.We then turn our attention to graphs for which the separability is given locally by the maximum intersection of the neighborhoods of any two non-adjacent vertices. We prove that all (house, hole)-free graphs fulfill this property — a class properly including the chordal graphs and the distance-hereditary graphs. We conclude that the separability can be computed in O(mΔ) time for such graphs.In the last part we introduce the concept of edge-separability, in analogy to edge-connectivity, and prove that the class of k-edge-separable graphs is closed under topological minors for any k. We explicitly give the forbidden topological minors of the k-edge-separable graphs for each 0≤k≤3.

Improvements of the Maximum Intersection Method for 3D Absolute Earthquake Locations

Wepresentanimprovementofthemaximumintersection(MAXI)method in which absolute earthquake location is defined by the maximum intersection number of hyperbolic equal differential time (EDT) volumes (one EDT volume being described as all grid nodes satisfying the arrival-time differences between two stations, a tolerance value known as TERR). This 3D technique is well adapted to a strongly heterogeneousenvironment,avoidsthedepthversusorigin-timetrade-off(evenusingP arrivals alone), and objectively filters possible erroneous arrival times. Improvements consist of introducing an iterative multiscale approach on the TERR parameter and conducting a hierarchy of grid discretization to refine the preliminary solution (multigrid algorithm). The outlier cleaning process is strengthened by conducting statistical analyses based on the number of EDT volume intersections per station, rather than on travel-time residues. Processing two series of synthetic arrival times computed in the 3D seismological configurationofthesouthernmostRyukyusubductionzone,offshoreTaiwan,allowsus to (1) confirm MAXI robustness, even when arrival times are highly disturbed or azimuthal coverage largely reduced, and (2) show that MAXI, by limiting trade-offs between origin time and depth and between epicentral position and depth, is less af- fected by a wrong velocity model than a technique that minimizes travel-time residues. To conclude, we apply the MAXI method to locate earthquakes recorded by the combined Central Weather Bureau of Taiwan (CWB) and the Japanese Meteorological Agency (JMA) networks (1991-2008) within a georealistic a priori 3D P-velocity model. Hypocenter determinations are selected based on MAXI confidence factors, and earthquake clustering along well-known tectonic features witnesses hypocenter determination accuracy.

On the inapproximability of maximum intersection problems

Given u sets, we want to choose exactly k sets such that the cardinality of their intersection is maximized. This is the so-called MAX-k-INTERSECT problem. We prove that MAX-k-INTERSECT cannot be approximated within an absolute error of 12n1−2ϵ+O(n1−3ϵ) unless P=NP. This answers an open question about its hardness. We also give a correct proof of an inapproximable result by Clifford and Popa (2011) [3] by proving that MAX-INTERSECT problem is equivalent to the MAX-CLIQUE problem.

Rupture at the flank of the subducted Gagua ridge: The 18 December 2001 earthquake (Mw 6.8) offshore eastern Taiwan

The southern Ryukyus represents an area where different tectonic stress regimes result in high seismicity and increased seismic hazard for nearby areas such as Taiwan. On 18 December 2001 at 04:03 (GMT) a strong earthquake (Mw 6.8) occurred in the forearc area of the southern Ryukyu subduction zone. Revised moment tensor solutions published by GCMT and BATS groups show a normal faulting mechanism with some strike-slip component and also point to a shallow focal depth (∼12 km). We use arrival times picked at both Taiwanese and Japanese stations along with a 3D geo-realistic a priori velocity model in order to obtain accurate absolute locations for the mainshock and 153 of its aftershocks. Locations are derived by using the Maximum intersection (MAXI) algorithm which has been used in many previous seismicity studies in the southern Ryukyus. These improved locations indicate that the mainshock was caused by the failure of a NE–SW oriented fault that extends from the edge of the Nanao forearc sedimentary basin to the Ryukyu arc basement. Far-field P and SH waveforms of the mainshock recorded at stations surrounding the source and at distances 30–100°, were inverted for the purpose of investigating its rupture process. A non-negative least-squares inversion technique utilizing multiple time windows was used to derive the spatio-temporal slip distribution. The preferred slip distribution model shows that there is one large area of high slip (∼0.9 m) at 5–15 km depth that essentially represents the crystalline rocks of the Ryukyu arc basement. Another smaller area with lower slip (∼0.4 m) extends at 10–15 km depth beneath the Nanao basin. Most aftershocks are located in areas of low slip (<0.4 m) filling the regions of slip deficit. It is likely that the 18 December 2001 earthquake was caused by a stress field interaction generated by the oblique subduction of the Gagua ridge and the gravitational forces acting at its landward flank.

Randomly coloring simple hypergraphs

We study the problem of constructing a (near) uniform random proper q-coloring of a simple k-uniform hypergraph with n vertices and maximum degree Δ. (Proper in that no edge is mono-colored and simple in that two edges have maximum intersection of size one.) We show that if for some α < 1 we have Δ ⩾ n α and q ⩾ Δ ( 1 + α ) / k α then Glauber dynamics will become close to uniform in O ( n log n ) time from a random (improper) start. Note that for k > 1 + α − 1 we can take q = o ( Δ ) .

Super-simple group divisible designs with block size 4 and index 9

A design is said to be super-simple if the intersection of any two blocks has at most two elements. In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super-simple GDDs are useful in constructing super-simple BIBDs. The existence of super-simple ( 4 , λ ) ‐ GDDs has been determined for λ = 2 – 6 . In this paper, we investigate the existence of a super-simple (4,9)-GDD of group type g u and show that such a design exists if and only if u ≥ 4 , g ( u − 2 ) ≥ 18 and u ( u − 1 ) g 2 ≡ 0 (mod 4).

Super-simple balanced incomplete block designs with block size 4 and index 9

In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super-simple designs are also useful in constructing codes and designs such as superimposed codes and perfect hash families. The existence of super-simple ( v , 4 , λ ) -BIBDs have been determined for λ = 2 – 6 . In this paper, we investigate the existence of a super-simple ( v , 4 , 9 ) -BIBD and show that such a design exists if and only if v ≡ 0 , 1 ( mod 4 ) and v ⩾ 20 . Applications of the results to optical orthogonal codes are also mentioned.

Super-simple balanced incomplete block designs with block size 4 and index 5

In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super-simple designs are also useful in other constructions, such as superimposed codes and perfect hash families etc. The existence of super-simple ( v , 4 , λ ) -BIBDs have been determined for λ = 2 , 3 , 4 and 6. When λ = 5 , the necessary conditions of such a design are that v ≡ 1 , 4 ( mod 12 ) and v ≥ 13 . In this paper, we show that there exists a super-simple ( v , 4 , 5 ) -BIBD for each v ≡ 1 , 4 ( mod 12 ) and v ≥ 13 .

The complexity of maximum matroid–greedoid intersection and weighted greedoid maximization

The maximum intersection problem for a matroid and a greedoid, given by polynomial-time oracles, is shown NP-hard by expressing the satisfiability of boolean formulas in 3-conjunctive normal form as such an intersection. The corresponding approximation problems are shown NP-hard for certain approximation performance bounds. Moreover, some natural parameterized variants of the problem are shown W[P]-hard. The results are in contrast with the maximum matroid–matroid intersection which is solvable in polynomial time by an old result of Edmonds. We also prove that it is NP-hard to approximate the weighted greedoid maximization within 2 n O ( 1 ) where n is the size of the domain of the greedoid.

Approximating centroids for the maximum intersection of spherical polygons

This paper considers the problem of investigating the spherical regions owned by the maximum number of spherical polygons. We present a practical O( n( v+ I)) time algorithm for finding the approximating centroids for the maximum intersection of spherical polygons, where n, v, and I are, respectively, the numbers of polygons, all vertices, and intersection points. In order to elude topological errors and handle geometric degeneracies, our algorithm takes the approach of edge-based partitioning of the sphere. Furthermore, the numerical complexity is avoided since the algorithm is completely spherical.

Quasi‐embeddings of Steiner triple systems, or Steiner triple systems of different orders with maximum intersection

AbstractIn this paper, we present a conjecture that is a common generalization of the Doyen–Wilson Theorem and Lindner and Rosa's intersection theorem for Steiner triple systems. Given u, v ≡ 1,3 (mod 6), u &lt; v &lt; 2u + 1, we ask for the minimum r such that there exists a Steiner triple system $(U,\,{\cal B}),\,|U|=u$ such that some partial system $(U,{\cal B}\,\backslash{\partial})$ can be completed to an STS$(v),\,(V,\,{\cal B}{^\prime})$, where |∂| = r. In other words, in order to “quasi‐embed” an STS(u) into an STS(v), we must remove r blocks from the small system, and this r is the least such with this property. One can also view the quantity (u(u − 1)/6) − r as the maximum intersection of an STS(u) and an STS(v) with u &lt; v. We conjecture that the necessary minimum r = (v − u) (2u + 1 − v)/6 can be achieved, except when u = 6t + 1 and v = 6t + 3, in which case it is r = 3t for t ≠ 2, or r = 7 when t = 2. Using small examples and recursion, we solve the cases v − u = 2 and 4, asymptotically solve the cases v − u = 6, 8, and 10, and further show for given v − u &gt; 2 that an asymptotic solution exists if solutions exist for a run of consecutive values of u (whose required length is no more than v − u). Some results are obtained for v close to 2u + 1 as well. The cases where ≈ 3u/2 seem to be the hardest. © 2004 Wiley Periodicals, Inc.

Hypocentre determination offshore of eastern Taiwan using the Maximum Intersection method

SUMMARY The maximum intersection (MAXI) method, which derives from the master station method (MSM), determines within a 3-D velocity model the absolute hypocentral location based on observed arrival times. First, the spatial node that better satisfies the arrival time differences computed at all station pairs, plus or minus an error tolerance value (in seconds), is defined as the preliminary hypocentral solution (PRED). Second, because PRED depends neither on the estimate of origin time nor on the residual root mean square (rms), residual outliers are objectively detected and cleaned out from the original data set without any iterative process or weighting. Third, a statistical minimization (residual rms) is conducted in a small domain around the PRED node, which results in a unique FINAL solution. The MAXI method is applied to the determination of earthquake hypocentres (with the proper station correction terms) in the southernmost extremity of the Ryukyu subduction zone, where several dense seismic clusters occur near the seismogenic plate interface. The location of earthquakes, recorded at both the Taiwanese and Japanese networks, is obtained for about a thousand events (between 1992 and 1997). The process uses a detailed 3-D velocity model based on multiple geophysical data sources obtained in the junction area between subduction and collision (east of Taiwan). The earthquake clustering and the significant drop in residual statistics (1.20, 0.80 and 0.35 s, for Taiwanese catalogue, MSM and MAXIM solutions respectively) indicate the accuracy of the method, which can be used to routinely determine absolute hypocentre location based on observed arrival times.

Approximating Centroids for the Maximum Intersection of Spherical Polygons

AbstractThis paper considers the problem of investigating the spherical regions owned by the maximum number of spherical polygons. We present a practical O(n(v+I)) time algorithm for finding the approximating centroids for the maximum intersection of spherical polygons, where n, v, and I are, respectively, the numbers of polygons, all vertices, and intersection points. In order to elude topological errors and handle geometric degeneracies, our algorithm takes the approach of edge-based partitioning of the sphere. Furthermore, the numerical complexity is avoided since the algorithm is completely spherical.