Ioannis Milis

Approximation schemes for minimizing average weighted completion time with release dates

We consider the problem of scheduling n jobs with release dates on m machines so as to minimize their average weighted completion time. We present the first known polynomial time approximation schemes for several variants of this problem. Our results include PTASs for the case of identical parallel machines and a constant number of unrelated machines with and without preemption allowed. Our schemes are efficient: for all variants the running time for /spl alpha/(1+/spl epsiv/) approximation is of the form f(1//spl epsiv/, m)poly(n).

Scheduling UET-UCT series-parallel graphs on two processors

Abstract The scheduling of task graphs on two identical processors is considered. It is assumed that tasks have unit-execution-time, and arcs are associated with unit-communication-time delays. The problem is to assign the tasks to the two processors and schedule their execution in order to minimize the makespan. A quadratic algorithm is proposed to compute an optimal schedule for a class of series-parallel graphs, called SP1 graphs, which includes in particular in-forests and out-forests.

Scheduling in Switching Networks with Set-Up Delays

We consider the (preemptive bipartite scheduling problem PBS) (Crescenzi et al., “On approximating a scheduling problem,” Journal of Combinatorial Optimization, vol. 5, pp. 287–297, 2001) arising in switching communication systems, where each input and output port can be involved in at most one communication at the same time. Given a set of communication tasks to be communicated from the transmitters to the receivers of such a system, we aim to find a schedule minimizing the overall transmission time. To achieve this, we allow the preemption of communication tasks. However, in practice preemption comes with a cost, d, and this renders the problem NP-hard (Gopal et al., “An optimal switching algorithm for multibeam satellite systems with variable bandwidth beams,” IEEE Trans. Commun., vol.30, pp. 2475–2481, 1982). In this paper, we present a

Speed scaling with power down scheduling for agreeable deadlines

2 - \frac{1}{d+1}

The densest k-subgraph problem on clique graphs

approximation algorithm, which is the first one for the PBS problem with approximation ratio strictly less than two. Furthermore, we propose a simple optimal polynomial time algorithm for a subclass of instances of the PBS problem.

Exact and approximation algorithms for densest k-subgraph

The densest k-subgraph (DkS) problem asks for a k-vertex subgraph of a given graph with the maximum number of edges. The DkS problem is NP-hard even for special graph classes including bipartite, planar, comparability and chordal graphs, while no constant approximation algorithm is known for any of these classes. In this paper we present a 3-approximation algorithm for the class of chordal graphs. The analysis of our algorithm is based on a graph theoretic lemma of independent interest.

Speed scaling for maximum lateness

We consider the problem of scheduling on a single processor a given set of n jobs. Each job j has a workload wj and a release time r j. The processor can vary its speed and hibernate to reduce energy consumption. In a schedule minimizing overall consumed energy, it might be that some jobs complete arbitrarily far from their release time. So in order to guarantee some quality of service, we would like to impose a deadline d j = rj + F for every job j, where F is a guarantee on the flow time. We provide an O(n3) algorithm for the more general case of agreeable deadlines, where jobs have release times and deadlines and can be ordered such that for every i < j, both ri rj and di dj.

Energy Efficient Scheduling of MapReduce Jobs

We improve complexity bounds for energy-efficient non-preemptive scheduling problems for both the single processor and multi-processor cases. As energy conservation has become a major concern, traditional scheduling problems have been revisited in the past few years to take into account the energy consumption [1]. We consider the speed scaling setting introduced by Yao et al. [20] where a set of jobs, each with a release date, deadline and work volume, are to be scheduled on a set of identical processors. The processors may change speed as a function of time and the energy they consume is the \(\alpha \)th power of their speed integrated over time. The objective is then to find a feasible non-preemptive schedule which minimizes the total energy used.