In video-based point cloud compression (V-PCC), the partitioning of the Coding Unit (CU) has ultra-high computational complexity. Just Noticeable Difference Model (JND) is an effective metric to guide this process. However, in this paper, it is found that the performance of traditional JND model is degraded in V-PCC. For the attribute video, due to the pixel-filling operation, the capability of brightness perception is reduced for the JND model. For the geometric video, due to the depth filling operation, the capability of depth perception is degraded in the boundary area for depth based JND models (JNDD). In this paper, a joint JND model (J_JND) is proposed for the attribute video to improve the brightness perception capacity, and an occupancy map guided JNDD model (O_JNDD) is proposed for the geometric video to improve the depth difference estimation accuracy of the boundaries. Based on the two improved JND models, a fast V-PCC Coding Unit (CU) partitioning algorithm is proposed with adaptive CU depth prediction. The experimental results show that the proposed algorithm eliminates 27.46% of total coding time at the cost of only 0.36% and 0.75% Bjontegaard Delta rate increment under the geometry Point-to-Point (D1) error and attribute Luma Peak-signal-Noise-Ratio (PSNR), respectively.

Memory-efficient Internet Protocol (IP) lookup with high speed is essential to achieve link-speed packet forwarding in IP routers. The rapid growth of Internet traffic and the development of optical link technologies have made IP lookup a major performance bottleneck in core routers. In this paper, we propose a new IP route lookup architecture based on hardware called Prefix-Route Trie (PR-Trie), which supports both IPv4 and IPv6 addresses. In PR-Trie, we develop a novel structure called Overlapping Hybrid Trie (OHT) to perform fast longest-prefix-matching (LPM) based on Multibit-Trie (MT), and a hash-based level matching query used to achieve only one off-chip memory access per lookup. In addition, the proposed PR-Trie also supports fast incremental updates. Since the memory complexity in MT-based IP lookup schemes depends on the level-partitioning solution and the data structure used, we develop an optimization algorithm called Bitmap-based Prefix Partitioning Optimization (BP2O). The proposed BP2O is based on a heuristic search using Ant Colony Optimization (ACO) algorithms to optimize memory efficiency. Experimental results using real-life routing tables prove that our proposal has superior memory efficiency. Theoretical performance analyses show that PR-Trie outperforms the classical Trie-based IP lookup algorithms.

Geometric partitioning mode (GPM) is a new inter prediction tool adopted in versatile video coding (VVC), which is the latest video coding of international standard developed by joint video expert team in 2020. Different from the regular inter prediction performed on rectangular blocks, GPM separates a coding block into two regions by the pre-defined 64 types of straight lines, generates inter predicted samples for each separated region, and then blends them to obtain the final inter predicted samples. With this feature, GPM improves the prediction accuracy at the boundary between the foreground and background with different motions. However, GPM has room to further improve the prediction accuracy if the final predicted samples can be generated using not only inter prediction but also intra prediction. In this paper, we propose a GPM with inter and intra prediction to achieve further enhanced compression capability beyond VVC. To maximize the coding performance of the proposed method, we also propose the restriction of the applicable intra prediction mode number and the prohibition of applying the intra prediction to both GPM-separated regions. The experimental results show that the proposed method improves the coding performance gain by the conventional GPM method of VVC by 1.3 times, and provides an additional coding performance gain of 1% bitrate savings in one of the coding structures for low-latency video transmission where the conventional GPM method cannot be utilized.

Human gait analysis has been widely used in medical and health fields. It is essential to extract spatio-temporal gait features (e.g., single support duration, step length, and toe angle) by partitioning the gait phase and estimating the footprint position/orientation in such fields. Therefore, we propose a method to partition the gait phase given a foot position sequence using mutually constrained piecewise linear approximation with dynamic programming, which not only represents normal gait well but also pathological gait without training data. We also propose a method to detect footprints by accumulating toe edges on the floor plane during stance phases, which enables us to detect footprints more clearly than a conventional method. Finally, we extract four spatial/temporal gait parameters for accuracy evaluation: single support duration, double support duration, toe angle, and step length. We conducted experiments to validate the proposed method using two types of gait patterns, that is, healthy and mimicked hemiplegic gait, from 10 subjects. We confirmed that the proposed method could estimate the spatial/temporal gait parameters more accurately than a conventional skeleton-based method regardless of the gait pattern.

A universal interconnection network implements arbitrary interconnections among n terminals. This paper considers a problem to realize such a network using contact switches. When n=2, it can be implemented with a single switch. The number of different connections among n terminals is given by the Bell number B(n). The Bell number shows the total number of methods to partition n distinct elements. For n=2, 3, 4, 5 and 6, the corresponding Bell numbers are 2, 5, 15, 52, and 203, respectively. This paper shows a method to realize an n terminal universal interconnection network with $rac {3}{8}(n^2-1)$ contact switches when n=2m+1≥5, and $rac {n}{8}(3n+2)$ contact switches, when n=2m≥6. Also, it shows that a lower bound on the number of contact switches to realize an n-terminal universal interconnection network is ⌈log 2B(n)⌉, where B(n) is the Bell number.

This paper proposes an efficient server selection scheme in successive participation scenario with participating-domain segmentation. The scheme is utilized by distributed processing systems for real-time interactive communication to suppress the communication latency of a wide-area network. In the proposed scheme, users participate for server selection one after another. The proposed scheme determines a recommended server, and a new user selects the recommended server first. Before each user participates, the recommended servers are determined assuming that users exist in the considered regions. A recommended server is determined for each divided region to minimize the latency. The new user selects the recommended available server, where the user is located. We formulate an integer linear programming problem to determine the recommended servers. Numerical results indicate that, at the cost additional computation, the proposed scheme offers smaller latency than the conventional scheme. We investigate different policies to divide the users' participation for the recommended server finding process in the proposed scheme.

Due to most of the existing graph repartitioning methods are known for poor efficiency in distributed environments. In this paper, we introduce a new graph repartitioning method with two phases in distributed environments. In the first phase, a local method is designed to identify all the potential candidate vertices that should be moved to the other partitions at once in each partition locally. In the second phase, a streaming graph processing model is adopted to reassign the candidate vertices to achieve lightweight graph repartitioning. During the reassignment of the vertex, we propose an objective function to balance both the load balance and the number of crossing edges among the distributed partitions. The experimental results with a large set of real word and synthetic graph datasets show that the communication cost can be reduced by nearly 1 to 2 orders of magnitude compared with the existing methods.

In the upcoming video coding standard VVC (Versatile Video Coding, H.266), a new coding block structure named quadtree nested multi-type trees (MTT) has been proposed. Compared with the quadtree structure defined in HEVC (High Efficiency Video Coding), the partition structure of MTT can achieve better coding performance. Since the splitting scheme of a CU (Coding Unit) need to be calculated recursively, the computational complexity is significantly increased. To reduce computational complexity as well as maintain compression performance, a fast multi-type tree decision algorithm is proposed. The application of binary and ternary tree in horizontal or vertical direction is found to be closely related to the characteristics of CU in this paper, and a metric named pixel difference of sub-blocks (SBPD) is defined to measure the characteristics of CU in different splitting type. By comparing the SBPD in horizontal and vertical sub-blocks, the selection of binary and ternary tree can be decided in advance, so as to skip some redundant splitting modes. Experimental results show that compared with the original reference software VTM 4.0, the average time saving of the proposed algorithm is 27% and the BD-rate is only increased by 0.55%.

The emerging Versatile Video Coding (VVC) standard currently adopts Triangular Partitioning Mode (TPM) to make more flexible inter prediction. Due to the motion search and motion storage for TPM, the complexity of the encoder and decoder is significantly increased. This letter proposes two simplifications of TPM for reducing the complexity of the current design. One simplification is to reduce the number of combinations of motion vectors for both partitions to be checked. The method gives 4% encoding time decrease with negligible BD-rate loss. Another one is to remove the reference picture remapping process in the motion vector storage of TPM. It reduces the complexity of the encoder and decoder without a BD-rate change for the random-access configuration.

A triangle enumerating problem is one of fundamental problems of graph data. Although several triangle enumerating algorithms based on MapReduce have been proposed, they still suffer from generating a lot of intermediate data. In this paper, we propose the efficient MapReduce algorithms to enumerate every triangle in the massive graph based on a vertex partition. Since a triangle is composed of an edge and a wedge, our algorithms check the existence of an edge connecting the end-nodes of each wedge. To generate every triangle from a graph in parallel, we first split a graph into several vertex partitions and group the edges and wedges in the graph for each pair of vertex partitions. Then, we form the triangles appearing in each group. Furthermore, to enhance the performance of our algorithm, we remove the duplicated wedges existing in several groups. Our experimental evaluation shows the performance of our proposed algorithm is better than that of the state-of-the-art algorithm in diverse environments.

In recent years we have witnessed an increasing demand to process queries on large datasets in Non-ordered Discrete Data Spaces (NDDS). In particular, one type of query in an NDDS, called box queries, is used in many emerging applications including error corrections in bioinformatics and network intrusion detection in cybersecurity. Effective indexing methods are necessary for efficiently processing queries on large datasets in disk. However, most existing NDDS indexing methods were not designed for box queries. Several recent indexing methods developed for box queries on a large NDDS dataset in disk are based on the popular data-partitioning approach. Unfortunately, a space-partitioning based indexing scheme, which is more effective for box queries in an NDDS, has not been studied before. In this paper, we propose a novel indexing method based on space-partitioning, called the BINDS-tree, for supporting efficient box queries on a large NDDS dataset in disk. A number of effective strategies such as node split based on minimum span and cross optimal balance, redundancy reduction utilizing a singleton dimension inheritance property, and a space-efficient structure for the split history are incorporated in the constructing algorithm for the BINDS-tree. Experimental results demonstrate that the proposed BINDS-tree significantly improves the box query I/O performance, comparing to that of the state-of-the-artdata-partitioning based NDDS indexing method.

In this paper, we consider a uniform bipartition problem in a population protocol model. The goal of the uniform bipartition problem is to divide a population into two groups of the same size. We study the problem under global fairness with various assumptions: 1) a population with or without a base station, 2) symmetric or asymmetric protocols, and 3) designated or arbitrary initial states. As a result, we completely clarify solvability of the uniform bipartition problem under global fairness and, if solvable, show the tight upper and lower bounds on the number of states.

Several types of capacitive crosstalk avoidance codes have been devised in order to prevent capacitive crosstalk in on-chip buses. These codes are designed to prohibit transition patterns prone to capacitive crosstalk from any two consecutive words transmitted to on-chip buses. The present paper provides a rigorous analysis of the asymptotic rate for (p,q)-transition free word sequences under the assumption that coding is based on a stateful encoder and a stateless decoder. Here, p and q represent k-bit transition patterns that should not appear in any two consecutive words at the same adjacent k-bit positions. The maximum rate for the sequences is proven to be equal to the subgraph domatic number of the (p,q)-transition free graph. Based on the theoretical results for the subgraph domatic partition problem, lower and upper bounds on the asymptotic rate are derived. We also show that the asymptotic rate 0.8325 is achievable for p=01 and q=10 transition free word sequences.

Computing the partition function of the Ising model on a graph has been investigated from both sides of computer science and statistical physics, with producing fertile results of P cases, FPTAS/FPRAS cases, inapproximability and intractability. Recently, measurement-based quantum computing as well as quantum annealing open up another bridge between two fields by relating a tree tensor network representing a quantum graph state to a rank decomposition of the graph. This paper makes this bridge wider in both directions. An $O^*(2^{ rac{omega}{2} bw(G)})$-time algorithm is developed for the partition function on n-vertex graph G with branch decomposition of width bw(G), where O* ignores a polynomial factor in n and ω is the matrix multiplication parameter less than 2.37287. Related algorithms of $O^*(4^{rw( ilde{G})})$ time for the tree tensor network are given which are of interest in quantum computation, given rank decomposition of a subdivided graph $ ilde{G}$ with width $rw( ilde{G})$. These algorithms are parameter-exponential, i.e., O*(cp) for constant c and parameter p, and such an algorithm is not known for a more general case of computing the Tutte polynomial in terms of bw(G) (the current best time is O*(min{2n, bw(G)O(bw(G))})) with a negative result in terms of the clique-width, related to the rank-width, under ETH.

This paper studies a variant of the graph partitioning problem, called the evacuation planning problem, which asks us to partition a target area, represented by a graph, into several regions so that each region contains exactly one shelter. Each region must be convex to reduce intersections of evacuation routes, the distance between each point to a shelter must be bounded so that inhabitants can quickly evacuate from a disaster, and the number of inhabitants assigned to each shelter must not exceed the capacity of the shelter. This paper formulates the convexity of connected components as a spanning shortest path forest for general graphs, and proposes a novel algorithm to tackle this multi-objective optimization problem. The algorithm not only obtains a single partition but also enumerates all partitions simultaneously satisfying the above complex constraints, which is difficult to be treated by existing algorithms, using zero-suppressed binary decision diagrams (ZDDs) as a compressed expression. The efficiency of the proposed algorithm is confirmed by the experiments using real-world map data. The results of the experiments show that the proposed algorithm can obtain hundreds of millions of partitions satisfying all the constraints for input graphs with a hundred of edges in a few minutes.

In this study, we developed a new orthogonal partition concept for asymmetric orthogonal arrays and used it for the construction of orthogonal arrays for the first time. Permutation matrices and the Kronecker product were also successfully and skillfully used as our main tools. Hence, a new general iterative construction method for asymmetric orthogonal arrays of high strength was developed, and some new infinite families of orthogonal arrays of strength 3 and several new orthogonal arrays of strength 4, 5, and 6 were obtained.

Distributed control plane architecture has been employed in software-defined data center networks to improve the scalability of control plane. However, since the flow space is partitioned by assigning switches to different controllers, the network topology is also partitioned and the rule setup process has to invoke multiple controllers. Besides, the control load balancing based on switch migration is heavyweight. In this paper, we propose a lightweight load partition method which decouples the flow space from the network topology. The flow space is partitioned with hosts rather than switches as carriers, which supports fine-grained and lightweight load balancing. Moreover, the switches are no longer needed to be assigned to different controllers and we keep all of them controlled by each controller, thus each flow request can be processed by exactly one controller in a centralized style. Evaluations show that our scheme reduces rule setup costs and achieves lightweight load balancing.

Recently, the join processing of large-scale datasets in MapReduce environments has become an important issue. However, the existing MapReduce-based join algorithms suffer from too much overhead for constructing and updating the data index. Moreover, the similarity computation cost is high because the existing algorithms partition data without considering the data distribution. In this paper, we propose two grid-based join algorithms for MapReduce. First, we propose a similarity join algorithm that evenly distributes join candidates using a dynamic grid index, which partitions data considering data density and similarity threshold. We use a bottom-up approach by merging initial grid cells into partitions and assigning them to MapReduce jobs. Second, we propose a k-NN join query processing algorithm for MapReduce. To reduce the data transmission cost, we determine an optimal grid cell size by considering the data distribution of randomly selected samples. Then, we perform kNN join by assigning the only related join data to a reducer. From performance analysis, we show that our similarity join query processing algorithm and our k-NN join algorithm outperform existing algorithms by up to 10 times, in terms of query processing time.

With the recent explosion of geographic data generated by smartphones, sensors, and satellites, a data storage that can handle the massive volume of data and support high-computational spatial queries is becoming essential. Although key-value stores efficiently handle large-scale data, they are not equipped with effective functions for supporting geographic data. To solve this problem, in this paper, we present G-HBase, a high-performance geographical database based on HBase, a standard key-value store. To index geographic data, we first use Geohash as the rowkey in HBase. Then, we present a novel partitioning method, namely binary Geohash rectangle partitioning, to support spatial queries. Our extensive experiments on real datasets have demonstrated an improved performance with k nearest neighbors and range query in G-HBase when compared with SpatialHadoop, a state-of-the-art framework with native support for spatial data. We also observed that performance of spatial join in G-HBase is on par with SpatialHadoop and outperforms SJMR algorithm in HBase.

The k-edge-connectivity augmentation problem with multipartition constraints (kECAMP, for short) is defined by “Given a multigraph G=(V,E) and a multipartition π={V1,...,Vr} (r≥2) of V, that is, $V = igcup_{h = 1}^r V_h$ and Vi∩Vj=∅ (1≤i