Distributed Algorithms for Scheduling on Line and Tree Networks

We have a set of processors (or agents) and a set of graph networks defined over some vertex set. Each processor can access a subset of the graph networks. Each processor has a demand specified as a pair of vertices $$, along with a profit; the processor wishes to send data between $u$ and $v$. Towards that goal, the processor needs to select a graph network accessible to it and a path connecting $u$ and $v$ within the selected network. The processor requires exclusive access to the chosen path, in order to route the data. Thus, the processors are competing for routes/channels. A feasible solution selects a subset of demands and schedules each selected demand on a graph network accessible to the processor owning the demand; the solution also specifies the paths to use for this purpose. The requirement is that for any two demands scheduled on the same graph network, their chosen paths must be edge disjoint. The goal is to output a solution having the maximum aggregate profit. Prior work has addressed the above problem in a distibuted setting for the special case where all the graph networks are simply paths (i.e, line-networks). Distributed constant factor approximation algorithms are known for this case. The main contributions of this paper are twofold. First we design a distributed constant factor approximation algorithm for the more general case of tree-networks. The core component of our algorithm is a tree-decomposition technique, which may be of independent interest. Secondly, for the case of line-networks, we improve the known approximation guarantees by a factor of 5. Our algorithms can also handle the capacitated scenario, wherein the demands and edges have bandwidth requirements and capacities, respectively.Comment: Accepted to PODC 2012, full versio

New benchmark results for the resource-constrained project scheduling problem.

This paper reports on computational results obtained with an updated version of the branch-and-bound procedure previously developed by Demeulemeester and Herroelen (1992) for solving the resource-constrained project scheduling problem (RCPSP). The new code fully exploits the advantages of 32-bit programming provided by recent compilers running on platforms such as Windows NT and OS/2 : flat memory, increased addressable memory and fast program execution. We study the impact of three important variables on the computation time for the RCPSP: addressable computer memory, the search strategy (depth-first, best-first or hybrid) and the introduction of an improved lower bound. We compare the results obtained by a truncated branch-and-bound procedure with the results generated by the minimum slack time heuristic and report on the dependency of its solution quality on the alotted CPU time.Scheduling; Project scheduling; Advantages; Studies;

Swing modulo scheduling: a lifetime-sensitive approach

This paper presents a novel software pipelining approach, which is called Swing Modulo Scheduling (SMS). It generates schedules that are near optimal in terms of initiation interval, register requirements and stage count. Swing Modulo Scheduling is an heuristic approach that has a low computational cost. The paper describes the technique and evaluates it for the Perfect Club benchmark suite. SMS is compared with other heuristic methods showing that it outperforms them in terms of the quality of the obtained schedules and compilation time. SMS is also compared with an integer linear programming approach that generates optimum schedules but with a huge computational cost, which makes it feasible only for very small loops. For a set of small loops, SMS obtained the optimum initiation interval in all the cases and its schedules required only 5% more registers and a 1% higher stage count than the optimumPeer ReviewedPostprint (published version

Resource-constrained project scheduling.

Abstract: Resource-constrained project scheduling involves the scheduling of project activities subject to precedence and resource constraints in order to meet the objective(s) in the best possible way. The area covers a wide variety of problem types. The objective of this paper is to provide a survey of what we believe are important recent in the area . Our main focus will be on the recent progress made in and the encouraging computational experience gained with the use of optimal solution procedures for the basic resource-constrained project scheduling problem (RCPSP) and important extensions. The RCPSP involves the scheduling of a project its duration subject to zero-lag finish-start precedence constraints of the PERT/CPM type and constant availability constraints on the required set of renewable resources. We discuss recent striking advances in dealing with this problem using a new depth-first branch-and-bound procedure, elaborating on the effective and efficient branching scheme, bounding calculations and dominance rules, and discuss the potential of using truncated branch-and-bound. We derive a set of conclusions from the research on optimal solution procedures for the basis RCPSP and subsequently illustrate how effective and efficient branching rules and several of the strong dominance and bounding arguments can be extended to a rich and realistic variety of related problems. The preemptive resource-constrained project scheduling problem (PRCPSP) relaxes the nonpreemption condition of the RCPSP, thus allowing activities to be interrupted at integer points in time and resumed later without additional penalty cost. The generalized resource-constrained project scheduling (GRCPSP) extends the RCPSP to the case of precedence diagramming type of precedence constraints (minimal finish-start, start-start, start-finish, finish-finish precedence relations), activity ready times, deadlines and variable resource availability's. The resource-constrained project scheduling problem with generalized precedence relations (RCPSP-GPR) allows for start-start, finish-start and finish-finish constraints with minimal and maximal time lags. The MAX-NPV problem aims at scheduling project activities in order to maximize the net present value of the project in the absence of resource constraints. The resource-constrained project scheduling problem with discounted cash flows (RCPSP-DC) aims at the same non-regular objective in the presence of resource constraints. The resource availability cost problem (RACP) aims at determining the cheapest resource availability amounts for which a feasible solution exists that does not violate the project deadline. In the discrete time/cost trade-off problem (DTCTP) the duration of an activity is a discrete, non-increasing function of the amount of a single nonrenewable resource committed to it. In the discrete time/resource trade-off problem (DTRTP) the duration of an activity is a discrete, non-increasing function of the amount of a single renewable resource. Each activity must then be scheduled in one of its possible execution modes. In addition to time/resource trade-offs, the multi-mode project scheduling problem (MRCPSP) allows for resource/resource trade-offs and constraints on renewable, nonrenewable and doubly-constrained resources. We report on recent computational results and end with overall conclusions and suggestions for future research.Scheduling; Optimal;

Harmonic scheduling of linear recurrences in digital filter design

Linear difference equations involving recurrences are fundamental equations that describe many important signal processing applications. For many high sample rate digital filter applications, we need to effectively parallelize the linear difference equations used to describe digital filters - a difficult task due to the recurrences inherent in the data dependences. We present a novel approach, Harmonic Scheduling, that exploits parallelism in these recurrences beyond loop-carried dependencies, and which generates optimal schedules for parallel evaluation of linear difference equations with resource constraints. This approach also enables us to derive a parallel schedule with minimum control overhead, given an execution time with resource constraints. We also present a Harmonic Scheduling algorithm that generates optimal schedules for digital filters described by second-order difference equations with resource constraints

A C-DAG task model for scheduling complex real-time tasks on heterogeneous platforms: preemption matters

Recent commercial hardware platforms for embedded real-time systems feature heterogeneous processing units and computing accelerators on the same System-on-Chip. When designing complex real-time application for such architectures, the designer needs to make a number of difficult choices: on which processor should a certain task be implemented? Should a component be implemented in parallel or sequentially? These choices may have a great impact on feasibility, as the difference in the processor internal architectures impact on the tasks' execution time and preemption cost. To help the designer explore the wide space of design choices and tune the scheduling parameters, in this paper we propose a novel real-time application model, called C-DAG, specifically conceived for heterogeneous platforms. A C-DAG allows to specify alternative implementations of the same component of an application for different processing engines to be selected off-line, as well as conditional branches to model if-then-else statements to be selected at run-time. We also propose a schedulability analysis for the C-DAG model and a heuristic allocation algorithm so that all deadlines are respected. Our analysis takes into account the cost of preempting a task, which can be non-negligible on certain processors. We demonstrate the effectiveness of our approach on a large set of synthetic experiments by comparing with state of the art algorithms in the literature

Instruction replication for clustered microarchitectures

This work presents a new compilation technique that uses instruction replication in order to reduce the number of communications executed on a clustered microarchitecture. For such architectures, the need to communicate values between clusters can result in a significant performance loss. Inter-cluster communications can be reduced by selectively replicating an appropriate set of instructions. However, instruction replication must be done carefully since it may also degrade performance due to the increased contention it can place on processor resources. The proposed scheme is built on top of a previously proposed state-of-the-art modulo scheduling algorithm that effectively reduces communications. Results show that the number of communications can decrease using replication, which results in significant speed-ups. IPC is increased by 25% on average for a 4-cluster microarchitecture and by as mush as 70% for selected programs.Peer ReviewedPostprint (published version