Path-Based Multicast Communication in Wormhole-Routed Unidirectional Torus Networks

This paper addresses the problem of one-to-many, or multicast, communication in wormhole-routed,n-dimensional torus networks. The proposed methods are designed for systems that support intermediate reception, which permits multidestination messages to be pipelined through several nodes, depositing a copy at each node. A key issue in the design of such systems is the routing function, which must support both unicast and multicast traffic while preventing deadlock among messages. An efficient, deadlock-free routing function is developed and used as a basis for a family of multicast algorithms. TheS-torusmulticast algorithm uses a single multidestination message to perform an arbitrary multicast operation. TheM-torusalgorithm is a generalized multiphase multicast algorithm, in which a combination of multidestination messages is used to perform a multicast in one or more communication steps. Two specific instances of the M-torus algorithm, theM_d-torusandM_u-torusmulticast algorithms, are presented. These algorithms produce contention-free multicast operations and are deadlock-free under all combinations of network traffic. A simulation study compares the performance of the different multicast algorithms, and implementation issues are discussed. The results of this research are applicable to the design of architectures for both wormhole-routed massively parallel computers and high-speed local area networks with wormhole-routed switch fabrics.     

Fast and proximity-aware multi-source overlay multicast under heterogeneous environment

Overlay multicast has been considered as one of the most important developments for the next generation Internet infrastructure. In this paper, we consider overlay multicast in the scenarios where any participant node is a potential data source. Existing multicast algorithms for single-source always require a long time to deliver messages or have high maintenance overhead when multiple data sources are allowed. There are other algorithms that are designed for multi-source scenarios. But they consume too much network resources and have a long convergence time because of proximity ignorance. To address the issues, we present FPCast, which leverages node heterogeneity and proximity information at the same time. Physically close nodes are grouped into clusters and each cluster selects a powerful, stable node as its rendezvous point. The rendezvous nodes form a DHT-based structure. Data messages are replicated and forwarded along implicit, source specific, and heterogeneity-aware multicast trees. We further reduce the delivery delay by introducing probabilistic forwarding scheme. We show the average delivery path length converges to O(logn) automatically (n is the number of nodes in the overlay). The simulation results demonstrate the superiority of our algorithm in terms of message delivery time and network resource consumption, in comparison with the previous randomized algorithms. The algorithm is also resilient to node failures.     

Multicasting in Generalized Multistage Interconnection Networks

Multistage interconnection networks (MIN) are popular in switching and communication applications. It is also well known as a hypercube derived architecture, offering a fixed-degree alternative to hypercube for a large class of applications. Message routing strategy in MIN is well known, however, multicasting issues for MIN has not been considered. This paper formulates the multicasting problem for MIN. We demonstrate that reordering the dimensions in MIN can lead to traffic reduced multicasting. This leads to the formulation of optimality criteria in MIN multicast operation. Traffic optimum multicasting in MIN is shown as a NP-Complete problem. We present a polynomial time greedy heuristic to generate traffic reduced multicast in MIN. The greedy approach generates a locally optimum solution. Analytical study and simulation results are presented showing the traffic reduction that can be obtained using our approach over traditional linearly ordered dimensions approach.     

Efficient architectures and algorithms for multicasting data in computer communication networks

This paper presents two network architectures with associated routing and multicast algorithms for improved performance under multicasting traffic conditions. A conditionally nonblocking network, referred to as a Clos network, forms the basis for the development of efficient multicast communication networks. The Clos network is first analyzed under multicast traffic conditions for blocking and multicast overflow probability. The analysis determines the overflow probability under two different multicast distribution assumptions. The first distribution assumes all packets request the same number of copies and the second distribution uses a random number of requested copies. An analysis of an extension of the presented network to multiplexed parallel planes of a network shows a significant improvement on the network performance and particularly on the carried traffic load when compared with previously published multicast architectures using different buffering strategies.     

A new high performance approach: merging optimal multicast sessions for supporting multisource routing

Each single source multicast session (SSMS) transmits packets from a source node s _i to a group of destination nodes t _i , i=1,2,…,n. An SSMS’s path can be established with a routing algorithm, which constructs multicast path between source and destinations. Also, for each SSMS, the routing algorithm must be performed once. When the number of SSMS increases to N≥2, the routing algorithm must be separately performed N≥2 times because the number of source nodes increase to N≥2 (for each SSMS the routing algorithm must be performed once). This causes that time of computation and bandwidth consumption to grow. To remove this problem, in this paper, we will present a new approach for merging different SSMSs to make a new multicast session, which is performed only with one execution of a routing algorithm. The new approach, merging different sessions together, is based on the optimal resource allocation and Constraint Based Routing (CBR). We will show that as compared to other available routing algorithms, it improves time of computation and bandwidth consumption and increases data rate and network efficiency. The new approach uses CBR and merges more than one single source multicast session (SSMS) problem to one multisource multicast session (MSMS) problem. By solving one MSMS problem instead of solving more than one SSMS, we can obtain an optimal solution that is more efficient than optimal solutions of SSMS problems.     

Dynamic fractional cascading

The problem of searching for a key in many ordered lists arises frequently in computational geometry. Chazelle and Guibas recently introduced fractional cascading as a general technique for solving this type of problem. In this paper we show that fractional cascading also supports insertions into and deletions from the lists efficiently. More specifically, we show that a search for a key inn lists takes timeO(logN +n log logN) and an insertion or deletion takes timeO(log logN). HereN is the total size of all lists. If only insertions or deletions have to be supported theO(log logN) factor reduces toO(1). As an application we show that queries, insertions, and deletions into segment trees or range trees can be supported in timeO(logn log logn), whenn is the number of segments (points).     

Ant based Pareto optimal solution for QoS aware energy efficient multicast in wireless networks

Most of the group communication technologies support real-time multimedia applications such as video conferencing and distributed gaming. These applications require quality-of-service (QoS) aware multicast routing protocol to deliver the same data stream to a predefined group of receivers. Since nodes in wireless networks are severely energy constrained due to finite battery source, hence it is of paramount importance that QoS aware multicast routing protocol be energy efficient. Transmission power control is one of the methods used to save energy. In this method, the nodes dynamically adjust the transmission power so that energy consumption in the tree is minimized. However, reduction in the transmission power increases the number of forwarding nodes in the multicast tree. This negatively impacts the QoS in terms of propagation delay, delay jitter, and packet loss etc. In wireless networks, there is a trade-off between the energy consumption and the QoS guarantees provided by the network. We unify these requirements into a multiobjective framework referred to as Energy Efficient QoS Multicast Routing (E²QoSMR). The goal is to simultaneously optimize the total power consumption and the QoS parameters in the multicast tree. We extend two algorithms based on metaphor of swarm intelligence for finding an energy efficient multicast tree satisfying the QoS guarantees. Extensive simulations have been conducted to validate the correctness and efficiency of the algorithms. The simulation result of the algorithms is compared with the nondominated sorting genetic algorithm, NSGA-III. The experimental results are consolidated by statistical analyses that demonstrate the ability of the algorithms to generate the Pareto optimal solution set.     

A new algorithm to prove the schedulability of real-time systems

In hard real-time multiprocessor systems, tasks not only have timing constraints but also often have precedence constraints caused by communication among themselves. In this paper a new algorithm to prove the schedulability of real-time systems is proposed, in which both precedence constraints and communication costs are considered and represented by offsets and modified deadlines. To obtain a tight upper bound for the worst-case response time, the concepts of local critical instant and local worst-case response time are introduced. The proposed algorithm is compared with other algorithms using test cases. The comparison shows that the proposed algorithm has improved the performances to these compared algorithms.     

YOMNA – An efficient deadlock-free multicast wormhole algorithm in 2-D mesh multicomputers

A mesh network is a popular architecture which has been implemented in many multicomputer systems. It is preferred because it offers useful edge connectivity and is partitioned into units that are still meshes. It is also scalable and has a number of features that make it particularly amenable to high-performance computing. The 2-D mesh topology has become increasingly important to multicomputer design because of its many desirable properties including scalability, low bandwidth and fixed degree of nodes.The essential pattern in new multicomputer generations is the multicast wormhole pattern, which corresponds to one-to-many communication in which one source sends the same message to multiple destination nodes. In wormhole routing, a message is decomposed into words or flits, and flits of one message may be spread out among several nodes. Deadlock in the interconnection network occurs when no message can advance towards its destination. Some deadlock-free routing algorithms for wormhole routing were proposed, but the network latency and the network traffic were not taken into consideration. An optimal message routing should achieve both minimum traffic and minimum latency for the communication patterns involved. Unfortunately, finding optimal message routing has been shown to be NP-hard for most common multicomputer topologies.In this paper, an efficient algorithm (YOMNA) is introduced to find a deadlock-free multicast wormhole routing in 2-D mesh parallel machines. YOMNA algorithm is a tree-based technique, in which the router simultaneously sends incoming flits on more than one outgoing channel. YOMNA algorithm is compared with the dual-path multicast routing, which is a path-based technique. YOMNA algorithm has proved to be deadlock free. The network latency and the network traffic are calculated for YOMNA algorithm and for the dual-path multicast routing. The results demonstrate that YOMNA algorithm outperformed the dual-path routing.     

Scalable 2D Convex Hull and Triangulation Algorithms for Coarse Grained Multicomputers

In this paper we describe scalable parallel algorithms for building the convex hull and a triangulation ofncoplanar points. These algorithms are designed for thecoarse grained multicomputermodel:pprocessors withO(n/p)⪢O(1) local memory each, connected to some arbitrary interconnection network. They scale over a large range of values ofnandp, assuming only thatn⩾p^1+ε(ε>0) and require timeO((T_sequential/p)+T_s(n, p)), whereT_s(n, p) refers to the time of a global sort ofndata on approcessor machine. Furthermore, they involve only a constant number of global communication rounds. Since computing either 2D convex hull or triangulation requires timeT_sequential=Θ(n log n) these algorithms either run in optimal time,Θ((n log n)/p), or in sort time,T_s(n, p), for the interconnection network in question. These results become optimal whenT_sequential/pdominatesT_s(n, p) or for interconnection networks like the mesh for which optimal sorting algorithms exist.     

On-line maintenance of triconnected components with SPQR-trees

We consider the problem of maintaining on-line the triconnected components of a graphG. Letn be the current number of vertices ofG. We present anO(n)-space data structure that supports insertions of vertices and edges, and queries of the type “Are there three vertex-disjoint paths between verticesv ₁ andv ₂?” A sequence ofk operations takes timeO(k·α(k, n)) ifG is biconnected(α(k, n) denotes the well-known Ackermann's function inverse), and timeO(n logn+k) ifG is not biconnected. Note that the bounds do not depend on the number of edges ofG. We use theSPQR-tree, a versatile data structure that represents the decomposition of a biconnected graph with respect to its triconnected components, and theBC-tree, which represents the decomposition of a connected graph with respect to its biconnected components.     

Demand-scalable geographic multicasting in wireless sensor networks

In this paper, we focus on the challenge of demand-scalable multicast routing in wireless sensor networks. Due to the ad-hoc nature of the placement of the sensor nodes as well as the variations in the available power of the nodes, centralized or stateful routing schemes are not applicable. Thus, in this paper, we first introduce a Geographic Multicast routing Protocol (GMP) for wireless sensor networks.¹ The protocol is fully distributed and stateless. Given a set of the destinations, the transmitting node first constructs a virtual Euclidean Steiner tree rooted at itself and including the destinations, using a novel and highly efficient reduction ratio heuristic (called rrSTR). The simulation results on NS2 show that GMP requires 25% less hops and energy than the existing Position Based Multicasting, PBM, Location-Guided Steiner trees, LGS, approaches. The GMP algorithm as well as LGS and PBM all assume that each recipient receives the same copy of the multicast message. In reality, however, especially when the transmission includes streamed media, different recipients have different demands (in terms of the frequency of packets or the quality of media). Thus, in this paper, we investigate the suitability of the geographic multicasting schemes for situations where scalable transmission paths can save power. In particular, we propose intuitive mechanisms to extend the three schemes to cases where the data transmission can scale based on the demand. This leads to three new weighted multicast routing algorithms: wGMP, wLGS, and wPBM. The results show that the wGMP algorithm provides the best opportunities for scalability due to its flexible self-correcting decision making process, while other schemes, such as wLGS and wPBM are not directly suitable for scalable multicasting, due to their naively greedy structures.     

Randomized Selection on the Hypercube

In this paper, we present randomized algorithms for selection on the hypercube. We identify two variants of the hypercube, namely, thesequential modeland theparallel model. In the sequential model, any node at any time can handle only communication along a single incident edge, whereas in the parallel model a node can communicate along all its incident edges at the same time. We specify three variations of the parallel model and present optimal randomized algorithms on all these three versions of parallel model. In particular, we show that selection on an input of sizencan be performed on ap-node hypercube in timeO((n/p) + logp) with high probability, on any of the three versions of the parallel model. This result is important in view of a lower bound that implies that selection needs Ω((n/p)log logp+ logp) time on ap-node sequential hypercube. We modify our selection algorithm to run on the sequential hypercube in which case it runs in an expected time nearly matching this lower bound. For the special case whenn=p, our selection algorithm runs in an optimalO(logn) time on the sequential hypercube. Our algorithms are very simple and are most likely to perform well in practice.     

Efficient triangulation of simple polygons

This paper considers the topic of efficiently traingulating a simple polygon with emphasis on practical and easy-to-implement algorithms. It also describes a newadaptive algorithm for triangulating a simplen-sided polygon. The algorithm runs in timeO(n(1+t _o)) witht ₀<n. The quantityt ₀ measures theshape-complexity of thetriangulation delivered by the algorithm. More preciselyt ₀ is the number of obtained triangles contained in the triangulation that share zero edges with the input polygon and is, furthermore, related to the shape-complexity of theinput polygon. Although the worst-case complexity of the algorithm isO(n ²), for several classes of polygons it runs in linear time. The practical advantages of the algorithm are that it is simple and does not require sorting or the use of balanced tree structures. On the theoretical side, it is of interest because it is the first polygon triangulation algorithm where thecomputational complexity is a function of theoutput complexity. As a side benefit, we introduce a new measure of the complexity of a polygon triangulation that should find application in other contexts as well.     

Computational geometry in a curved world

We extend the results of straight-edged computational geometry into the curved world by defining a pair of new geometric objects, thesplinegon and thesplinehedron, as curved generalizations of the polygon and polyhedron. We identify three distinct techniques for extending polygon algorithms to splinegons: the carrier polygon approach, the bounding polygon approach, and the direct approach. By these methods, large groups of algorithms for polygons can be extended as a class to encompass these new objects. In general, if the original polygon algorithm has time complexityO(f(n)), the comparable splinegon algorithm has time complexity at worstO(Kf(n)) whereK represents a constant number of calls to members of a set of primitive procedures on individual curved edges. These techniques also apply to splinehedra. In addition to presenting the general methods, we state and prove a series of specific theorems. Problem areas include convex hull computation, diameter computation, intersection detection and computation, kernel computation, monotonicity testing, and monotone decomposition, among others.     

Parallel Algorithms for Counting and Randomly Generating Integer Partitions

This paper presents parallel algorithms for determining the number of partitions of a given integerN, where the partitions may be subject to restrictions, such as being composed of distinct parts, of a given number of parts, and/or of parts belonging to a specified set. We present a series of adaptive algorithms suitable for varying numbers of processors. The fastest of these algorithms computes the number of partitions ofnwith largest part equal tok, for 1 ≤k≤n≤N, in timeO(log²(N)) usingO(N²/logN) processors. Parallel logarithmic time algorithms that generate partitions uniformly at random, using these quantities, are also presented.     

一种基于P2P的MMOG兴趣域内多播算法

提出了一种基于APOLO覆盖网络的支持MMOG的兴趣域内多播算法．玩家通过组内多播机制将游戏状态的更新通知给同一兴趣域中的其它玩家，从而维护玩家之间游戏状态的一致性．实验表明该算法能够在较大的程度上减小消息冗余和降低多播延迟．     

Computational performances of a simple interchange heuristic for a scheduling problem with an availability constraint

This paper deals with a scheduling problem on a single machine with an availability constraint. The problem is known to be NP-complete and admits several approximation algorithms. In this paper we study the approximation scheme described in He et al. [Y. He, W. Zhong, H. Gu, Improved algorithms for two single machine scheduling problems, Theoretical Computer Science 363 (2006) 257–265]. We provide the computation of an improved relative error of this heuristic, as well as a proof that this new bound is tight. We also present some computational experiments to test this heuristic on random instances. These experiments include an implementation of the fully-polynomial time approximation scheme given in Kacem and Ridha Mahjoub [I. Kacem, A. Ridha Mahjoub, Fully polynomial time approximation scheme for the weighted flow-time minimization on a single machine with a fixed non-availability interval, Computers and Industrial Engineering 56 (2009) 1708–1712].     

A new approach to estimating the expected first hitting time of evolutionary algorithms

Evolutionary algorithms (EA) have been shown to be very effective in solving practical problems, yet many important theoretical issues of them are not clear. The expected first hitting time is one of the most important theoretical issues of evolutionary algorithms, since it implies the average computational time complexity. In this paper, we establish a bridge between the expected first hitting time and another important theoretical issue, i.e., convergence rate. Through this bridge, we propose a new general approach to estimating the expected first hitting time. Using this approach, we analyze EAs with different configurations, including three mutation operators, with/without population, a recombination operator and a time variant mutation operator, on a hard problem. The results show that the proposed approach is helpful for analyzing a broad range of evolutionary algorithms. Moreover, we give an explanation of what makes a problem hard to EAs, and based on the recognition, we prove the hardness of a general problem.     

Multiple multicast with minimized node contention on wormhole k-aryn-cube networks

This paper presents a new approach to minimize node contention while performing multiple multicast/broadcast on wormhole k-ary n-cube networks with overlapped destination sets. The existing multicast algorithms in the literature deliver poor performance under multiple multicast because these algorithms have been designed with only single multicast in mind. The new algorithms introduced in this paper do not use any global knowledge about the respective destination sets of the concurrent multicasts. Instead, only local information and a source-specific partitioning approach are used. For systems supporting unicast message-passing, a new SPUmesh (Source-Partitioned Umesh) algorithm is proposed and is shown to be superior than the conventional Umesh algorithm for multiple multicast. Two different algorithms, SQHL (Source-Quadrant Hierarchical Leader) and SCHL (Source-Centered Hierarchical Leader), are proposed for systems with multidestination message-passing and shown to be superior than the HL scheme. All of these algorithms perform 1) 5-10 times faster than the existing algorithms under multiple multicast and 2) as fast as existing algorithms under single multicast. Furthermore, the SCHL scheme demonstrates that the latency of multiple multicast can, in fact, be reduced as the degree of multicast increases beyond a certain number. Thus, these algorithms demonstrate significant potential to be used for designing fast and scalable collective communication libraries on current and future generation wormhole systems