A random graph approach for multicast scheduling and performance analysis

Summary form only given. Multicast communication, which involves transmitting information from one node to multiple nodes, is a vital operation in both broadband integrated services digital networks (BISDN) and scalable parallel computers. Among different multicast switching networks, much work has been centered around the crossbar switches due to the simplicity of implementation. However, crossbars have the maximum number of crosspoints and implementation complexity among all switching fabrics. Multistage interconnect networks (MINs) such as Clos networks have attracted many attentions in recent years due to the nonblocking property as the crossbars, while at the same time possessing many advantages over crossbars. However, no multicast scheduling and routing algorithm have been applied to Clos network. This paper explores this aspect - we study some existing multicast scheduling and routing algorithms and apply them to Clos networks. Moreover, we propose two packet scheduling strategies to improve the system performance in terms of switch blocking probability and throughput, as shown by simulations.

A key issue in designing software multicast algorithms is to consider the trade-off between performance and portability. Portable software multicast algorithms based on generic communication models cannot capture some architecture-specific features. Without considering the underlying network architecture, these multicast algorithms may not achieve the truly optimal performance when implemented in real networks. The objective of this research is to investigate architecture-dependent tuning on performance of multicast algorithms developed based on architecture-independent models. Specifically, we intend to optimize the multicast algorithm based on the parameterized communication model. We propose two multicast algorithms, OPT-mesh and OPT-min which are the optimized versions of the parameterized multicast algorithm for wormhole-switched mesh networks and BMIN networks, respectively. Using our flit-level simulator the performance of both algorithms are compared with the architecture-independent version of the parameterized multicast algorithm and two other well-known network-dependent algorithms based on the binomial tree.

Multi-chip scheduler implementation in IQ switches are suited to reduce the hardware complexity in very large, high-speed, switches. However, this implies introducing a RTTs (Round Trip Time) among input and output selectors used to determine a matching due to inter-chip latency. This delay requires modifications to scheduling algorithms to allow a fully distributed implementation while keeping good performance. We propose a novel multicast scheduler, named IMRR, an extension of a previously proposed multicast scheduling algorithm named mRRM, making it suitable to a multi-chip implementation, and examine its performance by simulation.

We study subgraph counting over fully dynamic graphs, which undergo edge insertions and deletions. Counting subgraphs is a fundamental problem in graph theory with numerous applications across various fields, including database theory, social network analysis, and computational biology. In database theory, we can use dynamic subgraph counting algorithms on layered graphs to maintain the sizes of joins of databases that undergo updates. Specifically, the problem of finding the number of elements in a cyclic join of size k is equivalent to counting the number of k-cycles in k-layered graphs. For example, let R, S, and T be relations that have schemas (A, B), (B, C), and (C, A) respectively. Then the size of the join of R with S with T is given by the number of triangles in the corresponding layered graph where there is a layer for each attribute, the vertices are the attribute values and the edges represent the tuples of attribute values in the relations. Maintaining the number of triangles in fully dynamic graphs is very well studied and has an upper bound of O(√m) for the update time [KNN+20]. There is also a conditional lower bound of Ω(m 1/2-γ ) for any constant γ>0, for the update time [HKNS15] under the Online Matrix-Vector (OMv) conjecture implying that O(√m) is the ''right answer' for the update time of counting triangles. More recently, [HHH22] studied the problem of maintaining the number of 4-cycles in fully dynamic graphs and designed an algorithm with O(m 2/3 ) update time which is a natural generalization of the approach for counting triangles. They also studied the problem of counting 4-cliques showing that the folklore upper bound of O(m) for the update time is tight under the static combinatorial 4-clique conjecture by giving a lower bound of Ω(m 1-γ ) for any γ>0. Thus, it seems natural that O(m 2/3 ) might be the correct answer for the complexity of the update time for counting 4-cycles. In this work, we present an improved algorithm for maintaining the number of 4-cycles in fully dynamic graphs. Our algorithm achieves a worst-case update time of O(m 2/3-ε ) for some constant ε>0. We also show that the problem of counting 4-cycles is equivalent in layered graphs and general graphs. Our approach crucially uses fast matrix multiplication and leverages recent developments therein to get an improved runtime. Using the current best value of the matrix multiplication exponent ω=2.371339 we get ε=0.009811 and if we assume the best possible exponent i.e. ω=2 then we get ε=1/24. There is also a lower bound of Ω(m 1/2-γ ) for any constant γ>0, for the update time [HKNS15,HHH22], so there is still a big gap between the best-known upper and lower bounds. The key message of our paper is demonstrating that O(m 2/3 ) is not the correct answer for the complexity of the update time.

This paper considers the channel-assignment and scheduling in wireless mesh networks that employ multiple radios and multiple channels. In contrast to the various algorithms available in the literature, we explicitly model the delay overhead that is incurred during channel switching, and use that delay in the design of algorithms. We prove that the well known Greedy Maximal Scheduling (GMS) algorithm does not have any provable efficiency ratio when the switching overhead is considered. We present a centralized algorithm (CGSSO), and a dynamic algorithm (DMSSO), both of which consider switching overhead. Simulation results show that the proposed algorithms significantly outperform other algorithms in packet throughput and average packet delay metrics. Results also show that the improvements in performance become more pronounced as the switching delay increases.

This paper proposes a new reservation-based multicast scheduling algorithm which tries to make use of every data slot on all data channels such that the performance of the system is improved.

In the range emptiness searching problem, we are given a set P of n points in Rd, and wish to preprocess them into a data structure that supports efficient range emptiness queries, in which we specify a range σ, which is a semi-algebraic set in Rd of some fixed kind, and wish to determine whether P ∩ σ = θ. Range emptiness searching arises in many applications, and has been treated by Matousek [15] in the special case where the ranges are halfspaces bounded by hyperplanes. In this paper we extend the analysis to the general semi-algebraic case, and show how to adapt Matousek's technique to this case, without the need to linearize the ranges into a higher-dimensional space. This yields more efficient solutions to several interesting problems, and we demonstrate the new technique in two applications:(i) An algorithm for ray shooting amid balls in R3, which uses O* (n) storage and preprocessing, and answers a query in O* (n2/3) time, improving the previous bound of O* (n3/47).(ii) An algorithm that preprocesses, in O*(n) time, a set P of n points in R3 into a data structure with O*(n) storage, so that, for any query line l or segment e, the point of P farthest from l or from e can be computed in O* (n1/2) time.Our technique is closely related to the notions of nearest- or farthest-neighbor generalized Voronoi diagrams, and of the union or intersection of geometric objects, where sharper bounds on the combinatorial complexity of these structures yield faster range emptiness searching algorithms. For example, in the case of ray shooting amid balls, the structure that arises in our algorithm is the Euclidean Voronoi diagram of lines in 3-space, and the performance of the algorithm depends on the complexity of such diagrams (for which tight bounds are still unknown).

In this study, the objective of minimizing makespan has been considered for a scheduling problem of identical parallel machines with a single server and unavailability constraints. The unavailability constraints correspond to preventive maintenance periods. In this study, the jobs and the maintenance periods are scheduled simultaneously. This scheduling problem has a wide range of potential application areas in the manufacturing environment. In addition, the studied problem is a challenging one from theoretical point of view, due to its NP-Hardness. To conduct the study, a lower bound ( LB ) for the problem, and three metaheuristics namely Simulated Annealing ( SA ), Tabu Search ( TS ), and Genetic Algorithm ( GA ) have been proposed. The best parameters settings of the proposed algorithms were conducted using pilot runs with a Taguchi design. The algorithms performance has been assessed by using a set of test problems generated randomly. These test problems are based on a literature benchmark. The size of the instances, or number of jobs, were up to 500. Along with the performance analysis of the proposed algorithms, the effect of varying processing times and unavailability periods on the performance of the proposed algorithms is studied. The present work provides strong evidence of the efficiency and the performance of the proposed algorithms.

An on-line inventory problem is proposed and studied by our team differing from the traditional version of the problem, in which probability distributions for sales are supposed to know to the decision-maker, the on-line inventory problem of concern is due to the uncertainty where decision-makers only know the upper bound and lower bound of the daily demand for a particular product. The objective of game is to decide how many products should be prepared everyday so that the competitive ratio, which shows how close the on-line algorithm's performance to that of the relevant off-line optimal algorithm, can be minimized. First, a simplified on-line inventory problem model is formulated. Then, a competitive algorithm for general version of the problem, namely the general harmonic algorithm is presented. Furthermore the competitive ratio is proved to be the best one if decision-makers choose a fixed quantity product for any sequence of quantities from buyers. Finally, some other variants are also investigated and relevant competitive algorithms are developed.

The permutation flowshop scheduling problem with limited waiting time constraints, which requires that the waiting time of any job between two consecutive machines is not greater than a given upper bound, widely exists in the industrial manufacture with continuous production in high temperature environment or with intermediate products which are easily deteriorated. To explore an effective solving approach for the problem, some flowshop scheduling heuristics are extended for limited waiting time constraints and a comparison of those heuristics is carried out. Computational tests demonstrate the relationship between problem characteristics and algorithm performance, and show the adaptability of the heuristics.

Heterogeneous-ISA multi-core architectures have emerged as a promising design paradigm given the ever-increasing demands on single threaded performance. Such architectures comprise multiple cores that differ not just in micro-architectural parameters (e.g., fetch width, ROB size) but also in their Instruction Set Architectures (ISAs). These architectures extract previously latent performance gains by executing different phases of the program on the core (and ISA) best suited to it, as opposed to executing the entire program on a single ISA. In such a computing paradigm, maximum performance is only extracted when we ensure that at every point in the program’s execution, the program runs on the core best suited to it. In this work, we propose a migration framework that practically and accurately decides when to migrate the program across different cores (and ISAs) to extract maximum performance gains. Under the covers, this framework combines a regression based performance modelling technique with a greedy scheduling algorithm. Our performance modelling technique leverages hardware performance counters prevalent in all major processors today to accurately estimate the performance of the program on different ISAs to within an error of 6%. Putting it together with our greedy scheduler enables our framework to achieve single thread performance speedups of 29.6% with respect to a baseline single ISA heterogeneous architecture.

We present a methodology for automatically generating an online scheduling process for an arbitrary objective with the help of evolution strategies. The scheduling problem comprises independent parallel jobs and multiple identical machines and occurs in many real massively parallel processing systems. The system owner defines the objective that may consider job waiting times and priorities of user groups. Our scheduling process is a variant of the simple and commonly used greedy scheduling algorithm in combination with a repeated sorting of the waiting queue. This sorting uses a criterion whose parameters are evolutionary optimized. We evaluate our new scheduling process with real workload data and compare it to the best offline solutions and to the online results of the standard EASY backfill algorithm. To this end, we partition the user of the workloads into groups and select an exemplary objective that prioritizes some of those groups over others

We address the multicast problem in a wireless multihop network in the presence of errors. Finding the multicast schedule that minimizes the expected number of transmissions, while accounting for both the wireless broadcast advantage (WBA) and the wireless unreliable transmission (WUT) characteristics, has not been solved optimally before. We formally define the problem and propose an initial algorithm of non-polynomial complexity to obtain the optimal solution. The algorithm starts by transforming the wireless network topology into an auxiliary expanded graph that captures the WBA property, and assigning appropriate weights to the links so as to capture the WUT property. The proposed transformation is interesting on its own merit, since it permits us to consider only point-to-point transmissions (as in wireline networks) in the expanded graph, instead of the point-to-multipoint transmissions present in the original wireless network, and can also be useful in other optimization problems some of which we briefly describe. By solving the minimum Steiner tree problem on the expanded graph we obtain the optimal multicast solution for the initial graph. Since the optimal algorithm is of non-polynomial complexity, we also propose a number of heuristic algorithms. In particular, we first present a truncated graph transformation and then describe two heuristic algorithms for obtaining the multicast schedule. Simulation results show that the proposed heuristics have performance close to that of the optimal algorithm, at least for the instances for which we were able to track optimal solutions, while outperforming other heuristic multicast algorithms.

Distributed applications using file sharing and file replication, conferencing, and delivery in multimedia systems often need to use the semantics of causal multicast. Causal multicast in a mobile system is complicated by the various limitations imposed by the mobile system. Though there are different directions to improve the performance of causal multicast algorithms in mobile systems, at the core of such algorithms is the module to impose causal delivery among a set of nodes, which may be either mobile hosts, or mobile service stations, or peers at a higher level in the interconnection hierarchy. We show how to adapt the optimal causal multicast algorithm of Kshemkalyani-Singhal to mobile networks, and then show simulation results comparing its performance with that of other algorithms for causal multicast in mobile networks.

Many networking/computing applications require high speed switching for multicast traffic at the switch/router level to save network bandwidth. However, existing queueing based packet switches and scheduling algorithms cannot perform well under multicast traffic. While the speedup requirement makes the output queued switch difficult to scale, the single input queued switch suffers from the head of line (HOL) blocking, which severely limits the network throughput. An efficient yet simple buffering strategy to remove the HOL blocking is to use the virtual output queueing (VOQ), which has been shown to perform well under unicast traffic. However, it is impractical to use the traditional virtual output queued (VOQ) switches for multicast traffic, because a VOQ multicast switch has to maintain an exponential number of queues in each input port. We give a novel queue structure for the input buffers of a VOQ multicast switch by separately storing the address information and data information of a packet, so that an input port only needs to manage a linear number of queues. In conjunction with the multicast VOQ switch, we present a first-in-first-out based multicast scheduling algorithm, FIFO Multicast Scheduling (FIFOMS), and conduct extensive simulations to compare FIFOMS with other popular scheduling algorithms. Our results fully demonstrate the superiority of FIFOMS in both multicast latency and queue space requirement.