Csanád Imreh

Scheduling with Machine Cost

For most scheduling problems the set of machines is fixed initially and remains unchanged for the duration of the problem. We consider two basic online scheduling problems with the modification that initially the algorithm possesses no machines, but that at any point additional machines may be purchased. Upper and lower bounds on the competitive ratio are shown for both problems.

Online scheduling with machine cost and rejection

In this paper we define and investigate a new scheduling model. In this new model the number of machines is not fixed; the algorithm has to purchase the used machines, moreover the jobs can be rejected. We show that the simple combinations of the algorithms used in the area of scheduling with rejections and the area of scheduling with machine cost are not constant competitive. We present a 2.618-competitive algorithm called OPTCOPY.

Learning lexicographic orders

The purpose of this paper is to learn the order of criteria of lexicographic decision under various reasonable assumptions. We give a sample evaluation and an oracle based algorithm. In the worst case analysis we are dealing with the adversarial models. We show that if the distances of the samples are less than 4, then it is not learnable, but 4-distance samples are polynomial learnable.

The Buffer Minimization Problem for Multiprocessor Scheduling with Conflicts

We consider the problem of scheduling a sequence of tasks in a multi-processor system with conflicts. Conflicting processors cannot process tasks at the same time. At certain times new tasks arrive in the system, where each task specifies the amount of work (processing time) added to each processors workload. Each processor stores this workload in its input buffer. Our objective is to schedule task execution, obeying the conflict constraints, and minimizing the maximum buffer size of all processors. In the off-line case, we prove that, unless P = NP, the problem does not have a polynomial-time algorithm with a polynomial approximation ratio. In the on-line case, we provide the following results: (i) a competitive algorithm for general graphs, (ii) tight bounds on the competitive ratios for cliques and complete k-partite graphs, and (iii) a (Δ/2 + 1)-competitive algorithm for trees, where Δ is the diameter. We also provide some results for small graphs with up to 4 vertices.

Class constrained bin packing revisited

We study the following variant of the bin packing problem. We are given a set of items, where each item has a (non-negative) size and a color. We are also given an integer parameter k, and the goal is to partition the items into a minimum number of subsets such that for each subset S in the solution, the total size of the items in S is at most 1 (as in the classical bin packing problem) and the total number of colors of the items in S is at most k (which distinguishes our problem from the classical version). We follow earlier work on this problem and study the problem in both offline and online scenarios.

Scheduling problems on two sets of identical machines

In this paper we investigate the following scheduling problem: We have two sets of identical machines, the jobs have two processing times one for each set of machines. We consider two different objective functions, in the first model the goal is to minimize the maximum of the makespans on the sets, in the second model we minimize the sum of the makespans. We consider the online, semi online and offline versions of these problems.

Online strip packing with modifiable boxes

In the strip packing problem the goal is to pack a set of rectangles into a vertical strip so as to minimize the total height of the strip needed. We consider a modified version of the strip packing problem. In this version it is allowed to change the form of the rectangles by lengthening them, keeping the area fixed. We introduce online algorithms to solve this modified problem. Moreover a lower bound is presented, as well.

Online Clustering with Variable Sized Clusters

Online clustering problems are problems where the classification of points into sets (called clusters) is performed in an online fashion. Points arrive at arbitrary locations, one by one, to be assigned to clusters at the time of arrival. A point can be either assigned to an existing cluster or a new cluster can be opened for it. Here, we study a one-dimensional variant on a line. Each cluster is a closed interval, and there is no restriction on the length of a cluster. The cost of a cluster is the sum of a fixed set-up cost and its diameter (or length). The goal is to minimize the sum of costs of the clusters used by the algorithm.We study several variants, each having the two essential properties that a point which has been assigned to a given cluster must remain assigned to that cluster and no pair of clusters can be merged. In the strict variant, the diameter and the exact location of the cluster must be fixed when it is initialized. In the flexible variant, the algorithm can shift the cluster or expand it, as long as it contains all points assigned to it. In an intermediate model, the diameter is fixed in advance but the exact location can be modified. Here we give tight bounds on the competitive ratio of any online algorithm in each of these variants. In addition, for each model we also consider the semi-online case where points are presented ordered by their location.

Online scheduling with general machine cost functions

For most scheduling problems the set of machines is fixed initially and remains unchanged for the duration of the problem. Recently online scheduling problems have been investigated with the modification that initially the algorithm possesses no machines, but that at any point additional machines may be purchased. In all of these models the assumption has been made that each machine has unit cost. In this paper we consider the problem with general machine cost functions. Furthermore we also consider a more general version of the problem where the available machines have speed, the algorithm may purchase machines with speed 1 and machines with speed s. We define and analyze some algorithms for the solution of these problems and their special cases. Moreover we prove some lower bounds on the possible competitive ratios.

Online facility location with facility movements

In the online facility location problem demand points arrive one at a time and the goal is to decide where and when to open a facility. In this paper we consider a new version of the online facility location problem, where the algorithm is allowed to move the opened facilities in the metric space. We consider the uniform case where each facility has the same constant cost. We present an algorithm which is 2-competitive for the general case and we prove that it is 3/2-competitive if the metric space is the line. We also prove that no algorithm with smaller competitive ratio than