Joint Cache Partition and Job Assignment on Multi-Core Processors

Multicore shared cache processors pose a challenge for designers of embedded systems who try to achieve minimal and predictable execution time of workloads consisting of several jobs. To address this challenge the cache is statically partitioned among the cores and the jobs are assigned to the cores so as to minimize the makespan. Several heuristic algorithms have been proposed that jointly decide how to partition the cache among the cores and assign the jobs. We initiate a theoretical study of this problem which we call the joint cache partition and job assignment problem. By a careful analysis of the possible cache partitions we obtain a constant approximation algorithm for this problem. For some practical special cases we obtain a 2-approximation algorithm, and show how to improve the approximation factor even further by allowing the algorithm to use additional cache. We also study possible improvements that can be obtained by allowing dynamic cache partitions and dynamic job assignments. We define a natural special case of the well known scheduling problem on unrelated machines in which machines are ordered by "strength". Our joint cache partition and job assignment problem generalizes this scheduling problem which we think is of independent interest. We give a polynomial time algorithm for this scheduling problem for instances obtained by fixing the cache partition in a practical case of the joint cache partition and job assignment problem where job loads are step functions

Capacitated max-Batching with Interval Graph Compatibilities

We consider the problem of partitioning interval graphs into cliques of bounded size. Each interval has a weight, and the cost of a clique is the maximum weight of any interval in the clique. This natural graph problem can be interpreted as a batch scheduling problem. Solving an open question from [7, 4, 5], we show NP-hardness, even if the bound on the clique sizes is constant. Moreover, we give a PTAS based on a novel dynamic programming technique for this case.

An EPTAS for scheduling jobs on uniform processors using an MILP relaxation with a constant number of integral variables

We present an efficient polynomial time approximation scheme (EPTAS) for scheduling on uniform processors, i.e. finding a minimum length schedule for a set of n independent jobs on m processors with different speeds (a fundamental NP-hard scheduling problem). The previous best polynomial time approximation scheme (PTAS) by Hochbaum and Shmoys has a running time of (n/\epsilon)^{O(1/\epsilon^2)}. Our algorithm, based on a new mixed integer linear programming (MILP) formulation with a constant number of integral variables and an interesting rounding method, finds a schedule whose length is within a relative error $\epsilon$ of the optimum, and has running time 2^{O(1/\epsilon^2 \log(1/\epsilon)^3)} + poly(n)

Efficient Implementation of a Synchronous Parallel Push-Relabel Algorithm

Motivated by the observation that FIFO-based push-relabel algorithms are able to outperform highest label-based variants on modern, large maximum flow problem instances, we introduce an efficient implementation of the algorithm that uses coarse-grained parallelism to avoid the problems of existing parallel approaches. We demonstrate good relative and absolute speedups of our algorithm on a set of large graph instances taken from real-world applications. On a modern 40-core machine, our parallel implementation outperforms existing sequential implementations by up to a factor of 12 and other parallel implementations by factors of up to 3

Online Maximum k-Coverage

We study an online model for the maximum k-vertex-coverage problem, where given a graph G = (V,E) and an integer k, we ask for a subset A ⊆ V, such that |A | = k and the number of edges covered by A is maximized. In our model, at each step i, a new vertex vi is revealed, and we have to decide whether we will keep it or discard it. At any time of the process, only k vertices can be kept in memory; if at some point the current solution already contains k vertices, any inclusion of any new vertex in the solution must entail the irremediable deletion of one vertex of the current solution (a vertex not kept when revealed is irremediably deleted). We propose algorithms for several natural classes of graphs (mainly regular and bipartite), improving on an easy 1/2-competitive ratio. We next settle a set-version of the problem, called maximum k-(set)-coverage problem. For this problem we present an algorithm that improves upon former results for the same model for small and moderate values of k

Scheduling data flow program in xkaapi: A new affinity based Algorithm for Heterogeneous Architectures

Efficient implementations of parallel applications on heterogeneous hybrid architectures require a careful balance between computations and communications with accelerator devices. Even if most of the communication time can be overlapped by computations, it is essential to reduce the total volume of communicated data. The literature therefore abounds with ad-hoc methods to reach that balance, but that are architecture and application dependent. We propose here a generic mechanism to automatically optimize the scheduling between CPUs and GPUs, and compare two strategies within this mechanism: the classical Heterogeneous Earliest Finish Time (HEFT) algorithm and our new, parametrized, Distributed Affinity Dual Approximation algorithm (DADA), which consists in grouping the tasks by affinity before running a fast dual approximation. We ran experiments on a heterogeneous parallel machine with six CPU cores and eight NVIDIA Fermi GPUs. Three standard dense linear algebra kernels from the PLASMA library have been ported on top of the Xkaapi runtime. We report their performances. It results that HEFT and DADA perform well for various experimental conditions, but that DADA performs better for larger systems and number of GPUs, and, in most cases, generates much lower data transfers than HEFT to achieve the same performance

Alaraajojen lihasten spastisuus ennen ja jälkeen avustetun polkuharjoittelun

Opinnäytetyön tavoitteena oli kerätä tietoa aivoverenkiertohäiriötä, selkäydinvauriota sekä CP-vammaa sairastavien neurologisten asiakkaiden spastisten alaraajojen lihasten spastisuuden aiheuttaman lihasaktivaation mahdollisesta muutoksesta ennen ja jälkeen avustetulla polkulaitteella suoritetun polkuharjoituksen. Tarkoituksena oli tuottaa tutkittua tietoa kyseisen terapiamuodon vaikutuksesta edellä mainittuja oireyhtymiä sairastavien kuntoutuksessa. Toimeksiantaja voi hyödyntää tuloksia suunnitellessaan ja arvioidessaan neurologisten asiakkaiden kuntoutuksessa käytettäviä terapiamuotoja. Lisäksi tarkoituksena oli tuottaa fysioterapia-alalle tietoa terapiamuodon vaikutuksesta alaraajojen spastisuuteen. Työn tekijät syvensivät työn kautta omaa ammattitaitoaan tulevaa ammattia varten. Opinnäytetyömme tutkimusongelmana oli miten polkulaitteella suoritettu 20 minuutin avustettu polkuliike vaikuttaa aivoverenkiertohäiriötä, selkäydinvauriota sekä CP-vammaa sairastavien neurologisten asiakkaiden spastisuuden aiheuttamaan alaraajojen lihasaktivaatioon. Opinnäytetyö toteutettiin tapaustutkimuksena, johon osallistui viisi tutkimushenkilöä. Tutkimuksen aineisto kerättiin määrällisin menetelmin, joita olivat elektromyografia (EMG), Modified Modified Ashworth Scale (MMAS) sekä kysymyslomake. EMG ja MMAS mittaukset suoritettiin yhtäaikaisesta ennen polkuharjoitusta ja sen jälkeen. Mittareilla saadut tulokset analysoitiin MegaWin-ohjelmalla ja Microsoft Excel-taulukkolaskentaohjelmalla. Tulokset on esitetty numeerisessa ja graafisessa muodossa. Tutkimuksesta saatujen tulosten mukaan spastisuuden aiheuttama lihasaktivaatio väheni polkuharjoittelun jälkeen jokaisessa mitatussa lihaksessa EMG- ja MMAS -mittareilla mitattuna. Myös kysymyslomakkeella saatujen tulosten mukaan polkuharjoittelun vaikutukset spastisuuteen ovat positiivisia. Näin ollen tutkimustulosten perusteella avustetulla polkuharjoittelulla oli lihasten spastisuutta alentava vaikutus. Pienen tutkimusjoukon johdosta tuloksia ei voi kuitenkaan yleistää, mutta ne ovat suuntaa-antavia.The aim of this thesis is to gather information on possible changes in the spasticity of the lower limb muscles before and after assisted cycling exercise in clients with stroke, spinal cord injury and cerebral palsy. The purpose of this thesis is to produce information about the effects of the assisted cycling exercise in rehabilitation with clients suffering from the above mentioned injuries. The commissioner, Kemijärven Fysikaalinen Hoitolaitos Ky, can benefit from the achieved results while planning the rehabilitation of neurological clients. The authors’ purpose is to generate knowledge on the effects of assisted cycling exercise in spasticity of the lower limb muscles for physiotherapy field to use. The authors benefit from the thesis by obtaining their own expertise for the upcoming profession. The research problem of this thesis was to discover how the 20-minute assisted cycling exercise affects the spasticity of the lower limbs muscles in clients with stroke, spinal cord injury and cerebral palsy. This thesis is a case study in which participated five study subjects. The research data was gathered with the following quantitative methods: Electromyography (EMG), Modified Modified Ashworth Scale (MMAS) and questionnaire. EMG and MMAS were administrated simultaneously before and after assisted cycling exercise. The results were analysed with MegaWin-program and Microsoft Excel Spreadsheet. The results are displayed in numerical and graphical form. The results of this thesis show that after the assisted cycling exercise the muscle activation caused by spasticity, previously measured by EMG and MMAS, was reduced in every tested muscle. According to results from the questionnaire the effects of assisted cycling exercise was also positive. Therefore, it could be said that assisted cycling exercise reduces the spasticity in lower limb muscles. Due to the limited amount of participant in the study group, the results cannot be generalised, nevertheless, they can be used as directional information

Evaluation of Labeling Strategies for Rotating Maps

We consider the following problem of labeling points in a dynamic map that allows rotation. We are given a set of points in the plane labeled by a set of mutually disjoint labels, where each label is an axis-aligned rectangle attached with one corner to its respective point. We require that each label remains horizontally aligned during the map rotation and our goal is to find a set of mutually non-overlapping active labels for every rotation angle $\alpha \in [0, 2\pi)$ so that the number of active labels over a full map rotation of 2$\pi$ is maximized. We discuss and experimentally evaluate several labeling models that define additional consistency constraints on label activities in order to reduce flickering effects during monotone map rotation. We introduce three heuristic algorithms and compare them experimentally to an existing approximation algorithm and exact solutions obtained from an integer linear program. Our results show that on the one hand low flickering can be achieved at the expense of only a small reduction in the objective value, and that on the other hand the proposed heuristics achieve a high labeling quality significantly faster than the other methods.Comment: 16 pages, extended version of a SEA 2014 pape

Approximation Algorithms for the Capacitated Domination Problem

We consider the {\em Capacitated Domination} problem, which models a service-requirement assignment scenario and is also a generalization of the well-known {\em Dominating Set} problem. In this problem, given a graph with three parameters defined on each vertex, namely cost, capacity, and demand, we want to find an assignment of demands to vertices of least cost such that the demand of each vertex is satisfied subject to the capacity constraint of each vertex providing the service. In terms of polynomial time approximations, we present logarithmic approximation algorithms with respect to different demand assignment models for this problem on general graphs, which also establishes the corresponding approximation results to the well-known approximations of the traditional {\em Dominating Set} problem. Together with our previous work, this closes the problem of generally approximating the optimal solution. On the other hand, from the perspective of parameterization, we prove that this problem is {\it W[1]}-hard when parameterized by a structure of the graph called treewidth. Based on this hardness result, we present exact fixed-parameter tractable algorithms when parameterized by treewidth and maximum capacity of the vertices. This algorithm is further extended to obtain pseudo-polynomial time approximation schemes for planar graphs

Greedy D-Approximation Algorithm for Covering with Arbitrary Constraints and Submodular Cost

This paper describes a simple greedy D-approximation algorithm for any covering problem whose objective function is submodular and non-decreasing, and whose feasible region can be expressed as the intersection of arbitrary (closed upwards) covering constraints, each of which constrains at most D variables of the problem. (A simple example is Vertex Cover, with D = 2.) The algorithm generalizes previous approximation algorithms for fundamental covering problems and online paging and caching problems