Carolyn McCreary

A Comparison of Multiprocessor Scheduling Heuristics

Many algorithms for scheduling DAGs on multi-processors have been proposed, but there has been little work done to determine their effectiveness. Since multi-processor scheduling is an NP-hard problem, no exact tractible algorithm exists, and no baseline is available from which to compare the resulting schedules. Furthermore, performance guarantees have been found for only a few simple DAGs. This paper is an attempt to quantify the differences in five of the heuristics. Classification criteria are defined for the DAGs, and the differences between the heuristics are noted for various criteria. The comparison is made between a graph based method, two critical path methods, and two list scheduling heuristics. The empirical performance of the five heuristics is compared when they are applied to the randomly generated DAGs.

A comparison of heuristics for scheduling DAGs on multiprocessors

Many algorithms to schedule directed acyclic graphs (DAGs) on multiprocessors have been proposed, but there has been little work done to determine their effectiveness. Since multiprocessor scheduling is an NP-hard problem, no exact tractable algorithm exists, and no baseline is available from which to compare the resulting schedules. This paper is an attempt to quantify the differences in a few of the heuristics. The empirical performance of five heuristics is compared when they are applied to ten specific DAGs which represent program dependence graphs of important applications. The comparison is made between a graph based method a list scheduling technique and three critical path methods.<<ETX>>

Directed graphs drawing by Clan-based decomposition

This paper presents a system for automatically drawing directed graphs by using a graphanalysis that decomposes a graph into modules we call clans. Our system, CG (Clan-based Graph Drawing Tool), uses a unique clan-based graph decomposition to determine intrinsic subgraphs (clans) in the original graph and to produce a parse tree. The tree is given attributes that specify the node layout. CG then uses tree properties with the addition of “routing nodes” to route the edges. The objective of the system is to provide, automatically, an aesthetically pleasing visual layout for arbitrary directed graphs. Using the clan-based decomposition, CGs drawings are unique in several ways: (1)The node layout can be balanced both vertically and horizontally; (2) Nodes within a clan, a subgraph of nodes that have a common relationship with the rest of the nodes in the graph, are placed close to each other in the drawing; (3) Nodes are grouped according to a two-dimensional affinity rather than a single dimension such as level or rank [13]; (4) The users can contract a clan into a single node and later expand the node to show the subgraph in its original clan; and (5) Crossings reduction processing by clan-based graph decomposition is faster than Sugiyama, Tagawa, and Toda [20, 21] barycentric ordering algorithm.

Drawing Graphs with Attribute Graph Grammars

We address the problem of automatically generating layouts for graphs using graph grammars.

Broadcast communication delay metric for the iPSC/2 and iPSC/860 hypercubes

When determining the granularity of a program to be executed in parallel, it is important to have valid information on the cost of communication for the system on which the program is to be run. Previous studies have measured the node-to-node communication performance on the Intel Hypercube systems. This work measures the performance of multicast communication on the Intel iPSC/2 and iPSC/860 hypercubes and derives equations modelling the cost of broadcast communication.

Automatic partitioning and virtual scheduling for efficient parallel execution

The research of this report gives a method for automatic determination and scheduling of parallel modules from an existing sequential computation.In compiling a sequential program for execution on a multiprocessor system, there are four major problems to be solved: [26]1. Analyzing the data dependences and control dependences in the program.2. Identifying parallelism in the program.3. Partitioning the program into grains of sequential tasks.4. Scheduling the tasks on processors.The work of this paper addresses the last three problems. The automatic dependence analysis, the phase that detects where parallelism is constrained, has been studied extensively, and there exist a number of tools (e.g. PAT[3], PTOOL[2], Parafrase[21], Faust[19] and PTRAN[1]) that create data flow and control flow graphs from sequential code. A directed graph is typically used to model the dependence relation. Usually, a node of the graph G = (N,E) represents an operation such as a statement or block of statements, and an edge (u,v) represents the dependence of v on u, forcing the execution of u before v. For both data and control dependence, the key is to represent only essential dependence constraints as edges. This paper assumes that a dependence graph exists and discusses a method for performing the last three tasks on the dependence graph. The technique decomposes the data flow graph into grains of the appropriate size for any underlying homogeneous multiprocessor architecture, determines which grains should be executed in parallel and which must be executed sequentially, and schedules those grains onto processors.

An allocation algorithm for distributing Datalog programs

An O(N/sup 3/) algorithm for partitioning and allocating N Datalog procedural bundles among K distributed or dedicated processors is presented. The algorithm determines a static distribution of the bundles to all K processors. The independent variables of the objective function include both processing and communication costs, and the goal is to balance the processing requirements of the K processors while allocating bundles in such a way as to reduce the communication costs. The algorithm can be used with heterogeneous systems of processors, and it can accommodate a two-tier communication model in which both local area networks and more expensive wide area networks are used. The algorithm can be used interactively with a programmer or system designer. Example results from its implementation are given, and a comparison with another technique is shown. >