Marin Bougeret

Approximation algorithms for multiple strip packing

In this paper we study the Multiple Strip Packing (MSP) problem, a generalization of the well-known Strip Packing problem. For a given set of rectangles, r1,...,rn, with heights and widths ≤1, the goal is to find a non-overlapping orthogonal packing without rotations into k∈ℕ strips [0,1]×[0,∞), minimizing the maximum of the heights. We present an approximation algorithm with absolute ratio 2, which is the best possible, unless

A fast 5/2-approximation algorithm for hierarchical scheduling

{\cal P}={\cal NP}

Combining multiple heuristics on discrete resources

, and an improvement of the previous best result with ratio 2+e. Furthermore we present simple shelf-based algorithms with short running-time and an AFPTAS for MSP. Since MSP is strongly

Approximating the Non-contiguous Multiple Organization Packing Problem

{\cal NP}

Approximation Algorithms for the Wafer to Wafer Integration Problem

-hard, an FPTAS is ruled out and an AFPTAS is also the best possible result in the sense of approximation theory.

APPROXIMATION ALGORITHMS FOR MULTIPLE STRIP PACKING AND SCHEDULING PARALLEL JOBS IN PLATFORMS

We present in this article a new approximation algorithm for scheduling a set of n independent rigid (meaning requiring a fixed number of processors) jobs on hierarchical parallel computing platform. A hierarchical parallel platform is a collection of k parallel machines of different sizes (number of processors). The jobs are submitted to a central queue and each job must be allocated to one of the k parallel machines (and then scheduled on some processors of this machine), targeting theminimization of the maximum completion time (makespan). We assume that no job require more resources than available on the smallest machine. This problem is hard and it has been previously shown that there is no polynomial approximation algorithm with a ratio lower than 2 unless P = NP. The proposed scheduling algorithm achieves a 5/2 ratio and runs in O(log(npmax)knlog(n)), where pmax is the maximum processing time of the jobs. Our results also apply for the Multi Strip Packing problem where the jobs (rectangles) must be allocated on contiguous processors.

APPROXIMATING THE DISCRETE RESOURCE SHARING SCHEDULING PROBLEM

In this work we study the portfolio problem which is to find a good combination of multiple heuristics to solve given instances on parallel resources in minimum time. The resources are assumed to be discrete, it is not possible to allocate a resource to more than one heuristic. Our goal is to minimize the average completion time of the set of instances, given a set of heuristics on homogeneous discrete resources. This problem has been studied in the continuous case in [13]. We first show that the problem is hard and that there is no constant ratio polynomial approximation unless P = NP in the general case. Then, we design several approximation schemes for a restricted version of the problem where each heuristic must be used at least once. These results are obtained by using oracle with several guesses, leading to various tradeoff between the size of required information and the approximation ratio. Some additional results based on simulations are finally reported using a benchmark of instances on SAT solvers.

Improved approximation algorithms for scheduling parallel jobs on identical clusters

We present in this paper a Open image in new window -approximation algorithm for scheduling rigid jobs on multi-organizations. For a given set of n jobs, the goal is to construct a schedule for N organizations (composed each of m identical processors) minimizing the maximum completion time (makespan). This algorithm runs in O(n(N + log(n))log(np max )), where p max is the maximum processing time of the jobs. It improves the best existing low cost approximation algorithms. Moreover, the proposed analysis can be extended to a more generic approach which suggests different job partitions that could lead to low cost approximation algorithms of ratio better than Open image in new window .

Approximating the Sparsest k-Subgraph in Chordal Graphs

Motivated by the yield optimization problem in semi-conductor manufacturing, we model the wafer to wafer integration problem as a special multi-dimensional assignment problem (called WWI-m), and study it from an approximation point of view. We give approximation algorithms achieving an approximation factor of \(\frac{3}{2}\) and \(\frac{4}{3}\) for WWI-3, and we show that extensions of these algorithms to the case of arbitrary m do not give constant factor approximations. We argue that a special case of the yield optimization problem can be solved in polynomial time.

Tight Approximation for Scheduling Parallel Jobs on Identical Clusters

We consider two strongly related problems, multiple strip packing and scheduling parallel jobs in platforms. In the first one we are given a list of n rectangles with heights and widths bounded by one and N strips of unit width and infinite height. The objective is to find a nonoverlapping orthogonal packing without rotations of all rectangles into the strips minimizing the maximum height used. In the scheduling problem we consider jobs instead of rectangles, i.e., we are allowed to cut the rectangles vertically and we may have target areas of different size, called platforms. A platform Pl is a collection of ml processors running at speed sl and the objective is to minimize the makespan, i.e., the latest finishing time of a job.