Pfair scheduling of generalized pinwheel task systems

[[abstract]]The scheduling of generalized pinwheel task systems is considered. It is shown that pinwheel scheduling is closely related to the fair scheduling of periodic task systems. This relationship is exploited to obtain new scheduling algorithms for generalized pinwheel task systems. When compared to traditional pinwheel scheduling algorithms, these new algorithms are both more efficient from a run-time complexity point of view, and have a higher density threshold, on a very large subclass of generalized pinwheel task systems.

Route Planning in Transportation Networks

We survey recent advances in algorithms for route planning in transportation networks. For road networks, we show that one can compute driving directions in milliseconds or less even at continental scale. A variety of techniques provide different trade-offs between preprocessing effort, space requirements, and query time. Some algorithms can answer queries in a fraction of a microsecond, while others can deal efficiently with real-time traffic. Journey planning on public transportation systems, although conceptually similar, is a significantly harder problem due to its inherent time-dependent and multicriteria nature. Although exact algorithms are fast enough for interactive queries on metropolitan transit systems, dealing with continent-sized instances requires simplifications or heavy preprocessing. The multimodal route planning problem, which seeks journeys combining schedule-based transportation (buses, trains) with unrestricted modes (walking, driving), is even harder, relying on approximate solutions even for metropolitan inputs.Comment: This is an updated version of the technical report MSR-TR-2014-4, previously published by Microsoft Research. This work was mostly done while the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at Microsoft Research Silicon Valle

A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments

The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equation for neutral and ionic solutions, respectively. In the present work solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented to the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of a ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency, and allow for the treatment of different boundary conditions, as for example surface systems. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes

Trip-Based Public Transit Routing Using Condensed Search Trees

We study the problem of planning Pareto-optimal journeys in public transit networks. Most existing algorithms and speed-up techniques work by computing subjourneys to intermediary stops until the destination is reached. In contrast, the trip-based model focuses on trips and transfers between them, constructing journeys as a sequence of trips. In this paper, we develop a speed-up technique for this model inspired by principles behind existing state-of-the-art speed-up techniques, Transfer Pattern and Hub Labelling. The resulting algorithm allows us to compute Pareto-optimal (with respect to arrival time and number of transfers) 24-hour profiles on very large real-world networks in less than half a millisecond. Compared to the current state of the art for bicriteria queries on public transit networks, this is up to two orders of magnitude faster, while increasing preprocessing overhead by at most one order of magnitude

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;