Non-Clairvoyant Precedence Constrained Scheduling

We consider the online problem of scheduling jobs on identical machines, where jobs have precedence constraints. We are interested in the demanding setting where the jobs sizes are not known up-front, but are revealed only upon completion (the non-clairvoyant setting). Such precedence-constrained scheduling problems routinely arise in map-reduce and large-scale optimization. For minimizing the total weighted completion time, we give a constant-competitive algorithm. And for total weighted flow-time, we give an O(1/epsilon^2)-competitive algorithm under (1+epsilon)-speed augmentation and a natural "no-surprises" assumption on release dates of jobs (which we show is necessary in this context). Our algorithm proceeds by assigning virtual rates to all waiting jobs, including the ones which are dependent on other uncompleted jobs. We then use these virtual rates to decide on the actual rates of minimal jobs (i.e., jobs which do not have dependencies and hence are eligible to run). Interestingly, the virtual rates are obtained by allocating time in a fair manner, using a Eisenberg-Gale-type convex program (which we can solve optimally using a primal-dual scheme). The optimality condition of this convex program allows us to show dual-fitting proofs more easily, without having to guess and hand-craft the duals. This idea of using fair virtual rates may have broader applicability in scheduling problems

Bag-Of-Tasks Scheduling on Related Machines

We consider online scheduling to minimize weighted completion time on related machines, where each job consists of several tasks that can be concurrently executed. A job gets completed when all its component tasks finish. We obtain an $O(K^3 \log^2 K)$-competitive algorithm in the non-clairvoyant setting, where $K$ denotes the number of distinct machine speeds. The analysis is based on dual-fitting on a precedence-constrained LP relaxation that may be of independent interest.Comment: Preliminary version in APPROX 202

Energy-Efficient Multiprocessor Scheduling for Flow Time and Makespan

We consider energy-efficient scheduling on multiprocessors, where the speed of each processor can be individually scaled, and a processor consumes power $s^{\alpha}$ when running at speed $s$, for $\alpha>1$. A scheduling algorithm needs to decide at any time both processor allocations and processor speeds for a set of parallel jobs with time-varying parallelism. The objective is to minimize the sum of the total energy consumption and certain performance metric, which in this paper includes total flow time and makespan. For both objectives, we present instantaneous parallelism clairvoyant (IP-clairvoyant) algorithms that are aware of the instantaneous parallelism of the jobs at any time but not their future characteristics, such as remaining parallelism and work. For total flow time plus energy, we present an $O(1)$-competitive algorithm, which significantly improves upon the best known non-clairvoyant algorithm and is the first constant competitive result on multiprocessor speed scaling for parallel jobs. In the case of makespan plus energy, which is considered for the first time in the literature, we present an $O(\ln^{1-1/\alpha}P)$-competitive algorithm, where $P$ is the total number of processors. We show that this algorithm is asymptotically optimal by providing a matching lower bound. In addition, we also study non-clairvoyant scheduling for total flow time plus energy, and present an algorithm that achieves $O(\ln P)$-competitive for jobs with arbitrary release time and $O(\ln^{1/\alpha}P)$-competitive for jobs with identical release time. Finally, we prove an $\Omega(\ln^{1/\alpha}P)$ lower bound on the competitive ratio of any non-clairvoyant algorithm, matching the upper bound of our algorithm for jobs with identical release time

Greed Works -- Online Algorithms For Unrelated Machine Stochastic Scheduling

This paper establishes performance guarantees for online algorithms that schedule stochastic, nonpreemptive jobs on unrelated machines to minimize the expected total weighted completion time. Prior work on unrelated machine scheduling with stochastic jobs was restricted to the offline case, and required linear or convex programming relaxations for the assignment of jobs to machines. The algorithms introduced in this paper are purely combinatorial. The performance bounds are of the same order of magnitude as those of earlier work, and depend linearly on an upper bound on the squared coefficient of variation of the jobs' processing times. Specifically for deterministic processing times, without and with release times, the competitive ratios are 4 and 7.216, respectively. As to the technical contribution, the paper shows how dual fitting techniques can be used for stochastic and nonpreemptive scheduling problems.Comment: Preliminary version appeared in IPCO 201

Resource management algorithms for real-time wireless sensor networks with applications in cyber-physical systems

Wireless Sensor Networks (WSN) are playing a key role in the efficient operation of Cyber Physical Systems (CPS). They provide cost efficient solutions to current and future CPS re- quirements such as real-time structural awareness, faster event localization, cost reduction due to condition based maintenance rather than periodic maintenance, increased opportunities for real-time preventive or corrective control action and fine grained diagnostic analysis. However, there are several critical challenges in the real world applicability of WSN. The low power, low data rate characteristics of WSNs coupled with constraints such as application specified latency and wireless interference present challenges to their efficient integration in CPSs. The existing state of the art solutions lack methods to address these challenges that impediment the easy integration of WSN in CPS. This dissertation develops efficient resource management algorithms enabling WSNs to perform reliable, real-time, cost efficient monitoring. This research addresses three important problems in resource management in the presence of different constraints such as latency, precedence and wireless interference constraints. Additionally, the dissertation proposes a solution to deploy WSNs based real-time monitoring of critical infrastructure such as electrical overhead transmission lines. Firstly, design and analysis of an energy-aware scheduling algorithm encompassing both computation and communication subsystems in the presence of deadline, precedence and in- terference constraints is presented. The energy-delay tradeoff presented by the energy saving technologies such as Dynamic Voltage Scaling (DVS) and Dynamic modulation Scaling (DMS) is studied and methods to leverage it by way of efficient schedule construction is proposed. Performance results show that the proposed polynomial-time heuristic scheduling algorithm offers comparable energy savings to that of the analytically derived optimal solution. Secondly, design, analysis and evaluation of adaptive online algorithms leveraging run- time variations is presented. Specifically, two widely used medium access control schemes are considered and online algorithms are proposed for each. For one, temporal correlation in sensor measurements is exploited and three heuristics with varying complexities are proposed to perform energy minimization using DMS. For another, an adaptive algorithm is proposed addressing channel and load conditions at a node by influencing the selection of either low energy or low delay transmission option. In both cases, the simulation results show that the proposed schemes provide much better energy savings as compared to the existing algorithms. The third component presents design and evaluation of a WSN based framework to mon- itor a CPS namely, electrical overhead transmission line infrastructure. The cost optimized hybrid hierarchical network architecture is composed of a combination of wired, wireless and cellular technologies. The proposed formulation is generic and addresses constraints such as bandwidth and latency; and real world scenarios such as asymmetric sensor data generation, unreliable wireless link behavior, non-uniform cellular coverage and is suitable for cost minimized incremental future deployment. In conclusion, this dissertation addresses several challenging research questions in the area of resource management in WSNs and their applicability in future CPSs through associated algorithms and analyses. The proposed research opens up new avenues for future research such as energy management through network coding and fault diagnosis for reliable monitoring