Michel Cosnard

Compact DAG representation and its symbolic scheduling

Scheduling large task graphs is an important issue in parallel computing. In this paper we tackle the two following problems: (1) how to schedule a task graph, when it is too large to fit into memory? (2) How to build a generic program such that parameter values of a task graph can be given at run-time? Our answers feature the parameterized task graph (PTG), which is a symbolic representation of the task graph. We propose a dynamic scheduling algorithm which takes a PTG as an entry and allows us to generate a generic program. We present a theoretical study which shows that our algorithm finds good schedules for coarse-grain task graphs, has a low memory cost, and a low computational complexity. When the average number of operations of each task is large enough, we prove that the scheduling overhead is negligible with respect to the makespan. We also provide experimental results that demonstrate the feasibility of our approach using several compute-intensive kernels found in numerical scientific applications.

SLC: Symbolic scheduling for executing parameterized task graphs on multiprocessors

Task graph scheduling has been found effective in performance prediction and optimization of parallel applications. A number of static scheduling algorithms have been proposed for task graph execution on distributed memory machines. Such an approach cannot be adapted to changes in values of program parameters and the number of processors and also it cannot handle large task graphs. In this paper, we model parallel computation using parameterized task graphs which represent coarse-grain parallelism independent of the problem size. We present a scheduling algorithm for a parameterized task graph which first derives symbolic linear clusters and then assigns task clusters to processors. The runtime system executes clusters on each processor in a multi-threaded fashion. We evaluate our method using various compute-intensive kernels that can be found in scientific applications.

Powerful Resource Discovery for Arigatoni Overlay Network

Arigatoni is a structured multi-layer overlay network providing various services with variable guarantees, and promoting an intermittent participation in the overlay since peers can appear, disappear and organize themselves dynamically. Arigatoni provides fully decentralized, asynchronous and scalable resource discovery; it also provides mechanisms for dealing with an overlay with a dynamic topology. This paper introduces a nontrivial improvement of the resource discovery protocol by allowing the registration and request of multiple instances of the same service, service conjunctions, and multiple services. Adding multiple instances is a nontrivial task since the discovery protocol must keep track (when routing requests) of peers that accept to serve and peers that deny the service. Adding service conjunctions allows a single peer to offer different services at the same time. Simulations show that it is efficient and scalable.

Arigatoni: A Simple Programmable Overlay Network

We design a lightweight overlay network, called Arigatoni, that is suitable to deploy the global computing paradigm over the Internet. Communications over the behavioral units of the model are performed by a simple communication protocol. Basic global computers can communicate by first registering to a brokering service and then by mutually asking and offering services, in a way that is reminiscent to Rapoports tit-for-tat strategy of cooperation based on reciprocity. In the model, resources are encapsulated in the administrative domain in which they reside, and requests for resources located in another administrative domain traverse a broker-2-broker negotiation using classical PKI mechanisms. The model is suitable to fit with various global scenarios from classical P2P applications, like file sharing, or band-sharing, to more sophisticated grid applications, like remote and distributed big (and small) computations, to possible, futuristic real migrating computations. Indeed, our model fits some of the objectives suggested by the CoreGrid network of excellence, as described in Schwiegelshohn et al. (Schwiegelshohn et al., 2005)

Optimal Solution of the Maximum All Request Path Grooming Problem

We give an optimal solution to the Maximum All Request Path Grooming (MARPG) problem motivated by a traffic grooming application. The MARPG problem consists in finding the maximum number of connections which can be established in a path of size N, where each arc has a capacity or bandwidth C (grooming factor). We present a greedy algorithm to solve the problem and an explicit formula for the maximum number of requests that can be groomed. In particular, if C = s(s+1)/2 and N ge s(s-1), an optimal solution is obtained by taking all the requests of smallest length, that is of length 1 to s. However this is not true in general since anomalies can exist. We give a complete analysis and the exact number of such anomalies.

Virtual Organizations in Arigatoni

Arigatoni is a lightweight overlay network that deploys the Global Computing Paradigm over the Internet. Communication for over the behavioral units of the overlay is performed by a simple resource discovery protocol (RDP). Basic Global Computers Units (GC) can communicate by first registering to a brokering service and then by mutually asking and offering services. Colonies and communities are the main entities in the model. A colony is a simple virtual organization composed by exactly one leader and some set (possibly empty) of individuals. A community is a raw set of colonies and global computers (think it as a soup of colonies and global computer without a leader). We present an operational semantics via a labeled transition system, that describes the main operations necessary in the Arigatoni model to perform leader negotiation, joining/leaving a colony, linking two colonies and moving one GC from one colony to another. Our formalization results to be adequate w.r.t. the algorithm performing peer logging/delogging and colony aggregation.

Low memory cost dynamic scheduling of large coarse grain task graphs

Scheduling large task graphs is an important issue in parallel computing since it allows the treatment of large size problems. We tackle the following problem: how to schedule a task graph, when it is too large to fit into memory. Our answer features the parameterized task graph (PTG), which is a symbolic representation of the task graph. We propose a dynamic scheduling algorithm which takes the PTG as an entry and allows to generate a generic program. The performance of the method is studied as well as its limitations. We show that our algorithm finds a good schedule for coarse grain task graphs, has a very low memory cost, and has a good computational complexity. When the average number of operations of each task is large enough, we prove that the scheduling overhead is negligible with respect to the makespan. The feasibility of our approach is studied on several compute-intensive kernels found in numerical scientific applications.

Logical networks: towards foundations for programmable overlay networks and overlay computing systems

We propose and discuss foundations for programmable overlay networks and overlay computing systems. Such overlays are built over a large number of distributed computational individuals, virtually organized in colonies, and ruled by a leader (broker) who is elected or imposed by system administrators. Every individual asks the broker to log in the colony by declaring the resources that can be offered (with variable guarantees). Once logged in, an individual can ask the broker for other resources. Colonies can recursively be considered as evolved individuals who can log in an outermost colony governed by another (super)-broker. Communications and routing intra-colonies goes through a broker-2-broker PKI-based negotiation. Every broker routes intra- and inter- service requests by filtering its resource routing table, and then by forwarding the request first inside its colony, and second outside, via the proper super-broker (thus applying an endogenous-first-estrogen-last strategy). Theoretically, queries are formulae in first-order logic equipped with a small program used to orchestrate and synchronize atomic formulae. When the client individual receives notification of all (or part of) the requested resources, then the real resource exchange is performed directly by the server(s) individuals, without any further mediation of the broker, in a pure peer-to-peer fashion. The proposed overlay promotes an intermittent participation in the colony, since peers can appear, disappear, and organize themselves dynamically. This implies that the routing process may lead to failures, because some individuals have quit, or are temporarily unavailable, or they were logged out manu militari by the broker due to their poor performance or greediness. We design, validate through simulation, and implement these foundations in a programmable overlay computer system, called Arigatoni.

Using postordering and static symbolic factorization for parallel sparse LU

In this paper we present several improvements of widely used parallel LU factorization methods on sparse matrices. First we introduce the LU elimination forest and then we characterize the L, U factors in terms of their corresponding LU elimination forest. This characterization can be used as a compact storage scheme of the matrix as well as of the task dependence graph. To improve the use of BLAS in the numerical factorization, we perform a postorder traversal of the LU elimination forest, thus obtaining larger supernodes. To expose more task parallelism for a sparse matrix, we build a more accurate task dependence graph that includes only the least necessary dependences. Experiments compared favorably our methods against methods implemented in the S* environment on the SGIs Origin2000 multiprocessor.

Improving resource discovery in the Arigatoni overlay network

Arigatoni is a structured multi-layer overlay network providing various services with variable guarantees, and promoting an intermittent participation to the virtual organization where peers can appear, disappear and organize themselves dynamically. Arigatoni mainly concerns with how resources are declared and discovered in the overlay, allowing global computers to make a secure, PKI-based, use of global aggregated computational power, storage, information resources, etc. Arigatoni provides fully decentralized, asynchronous and scalable resource discovery, and provides mechanisms for dealing with dynamic virtual organizations. This paper introduces a non trivial improvement of the original resource discovery protocol by allowing to register and to ask for multiple instances. Simulations show that it is efficient and scalable.