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A Nearlinear Time Constant Factor Algorithm for Unsplittable Flow Problem on Line with Bag Constraints
"... Consider a scenario where we need to schedule a set of jobs on a system offering some resource (such as electrical power or communication bandwidth), which we shall refer to as bandwidth. Each job consists of a set (or bag) of job instances. For each job instance, the input specifies the start time, ..."
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Consider a scenario where we need to schedule a set of jobs on a system offering some resource (such as electrical power or communication bandwidth), which we shall refer to as bandwidth. Each job consists of a set (or bag) of job instances. For each job instance, the input specifies the start time, finish time, bandwidth requirement and profit. The bandwidth offered by the system varies at different points of time and is specified as part of the input. A feasible solution is to choose a subset of instances such that at any point of time, the sum of bandwidth requirements of the chosen instances does not exceed the bandwidth available at that point of time, and furthermore, at most one instance is picked from each job. The goal is to find a maximum profit feasible solution. We study this problem under a natural assumption called the nobottleneck assumption (NBA), wherein the bandwidth requirement of any job instance is at most the minimum bandwidth available. We present a simple, nearlinear time constant factor approximation algorithm for this problem, under NBA. When each job consists of only one job instance, the above problem is the same as the wellstudied unsplittable flow problem (UFP) on lines. A constant factor approximation algorithm is known for the UFP on line, under NBA. Our result leads to an alternative constant factor approximation algorithm for this problem. Though the approximation ratio achieved by our algorithm is inferior, it is much simpler, deterministic and faster in comparison to the existing algorithms. Our algorithm runs in nearlinear time (O(n log 2 n)), whereas the running time of the known algorithms is a high order polynomial. The core idea behind our algorithm is a reduction from the varying bandwidth case to the easier uniform bandwidth case, using a technique that we call slicing.
Approximation Algorithms for the Unsplittable Flow Problem on Paths and Trees
"... We study the Unsplittable Flow Problem (UFP) and related variants, namely UFP with Bag Constraints and UFP with Rounds, on paths and trees. We provide improved constant factor approximation algorithms for all these problems under the no bottleneck assumption (NBA), which says that the maximum demand ..."
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We study the Unsplittable Flow Problem (UFP) and related variants, namely UFP with Bag Constraints and UFP with Rounds, on paths and trees. We provide improved constant factor approximation algorithms for all these problems under the no bottleneck assumption (NBA), which says that the maximum demand for any sourcesink pair is at most the minimum capacity of any edge. We obtain these improved results by expressing a feasible solution to a natural LP relaxation of the UFP as a nearconvex combination of feasible integral solutions.
To Migrate or to Wait: BandwidthLatency Tradeoff In Opportunistic Scheduling of Parallel Tasks
"... AbstractWe consider the problem of scheduling lowpriority tasks onto resources already assigned to highpriority tasks. Due to burstiness of the highpriority workloads, the resources can be temporarily underutilized and made available to the lowpriority tasks. The increased level of utilization ..."
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AbstractWe consider the problem of scheduling lowpriority tasks onto resources already assigned to highpriority tasks. Due to burstiness of the highpriority workloads, the resources can be temporarily underutilized and made available to the lowpriority tasks. The increased level of utilization comes at a cost to the lowpriority tasks due to intermittent resource availability. Focusing on two major costs, bandwidth cost associated with migrating tasks and latency cost associated with suspending tasks, we aim at developing online scheduling policies achieving the optimal bandwidthlatency tradeoff for parallel lowpriority tasks with synchronization requirements. Under Markovian resource availability models, we formulate the problem as a Markov Decision Process (MDP) whose solution gives the optimal scheduling policy. Furthermore, we discover structures of the problem in the special case of homogeneous availability patterns that enable a simple thresholdbased policy that is provably optimal. We validate the efficacy of the proposed policies by tracedriven simulations. I.
1 IT Infrastructure for Providing EnergyasaService to Electric Vehicles
"... Abstract—Plugin Hybrid Electric Vehicles (PHEVs) are set to be the defining trend in road transportation for the 21st century. Unfortunately, the process of charging a large number of PHEVs will put a prohibitive amount of stress on conventional power grids. As per current estimates, it will not be ..."
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Abstract—Plugin Hybrid Electric Vehicles (PHEVs) are set to be the defining trend in road transportation for the 21st century. Unfortunately, the process of charging a large number of PHEVs will put a prohibitive amount of stress on conventional power grids. As per current estimates, it will not be possible to satisfy the peak demand of charging millions of PHEVs with current infrastructure. Additionally, to ensure stability of the power grid, the demand needs to be closely matched with supply all the time. This is difficult to ensure in a dynamic scenario like PHEV charging, where it is not possible to predict the load in the future. This problem is further complicated by the introduction of intermittent sources of alternate energy like wind power. This paper proposes an IT infrastructure for managing energy usage of PHEVs. The paper introduces a generalized currency of energy called a token, which entitles its owner to produce or consume a certain amount of electrical energy. Furthermore, the paper propose an IT infrastructure to manage tokens produced by millions of PHEVs and power stations. Simulation results for the system that consider the behavior of millions of PHEVs using data in prior work and traces from the Australian power grid for the last five years are also presented. Index Terms—PHEV scheduling, IT infrastructure, power distribution