An Improved Algorithm for Online Unit Clustering

We revisit the online unit clustering problem in one dimension which we recently introduced at WAOA’06: given a sequence of n points on the line, the objective is to partition the points into a minimum number of subsets, each enclosable by a unit interval. We present a new randomized online algorithm that achieves expected competitive ratio 11/6 against oblivious adversaries, improving the previous ratio of 15/8. This immediately leads to improved upper bounds for the problem in two and higher dimensions as well. A preliminary version of this paper appeared in the Proceedings of the 13th Annual International Computing and Combinatorics Conference (COCOON 2007), LNCS 4598, pp. 383–393.     

Online hypergraph coloring

In this paper we investigate the online hypergraph coloring problem. In this online problem the algorithm receives the vertices of the hypergraph in some order v₁,…,vn and it must color vi by only looking at the subhypergraph Hi=(Vi,Ei) where Vi={v₁,…,vi} and Ei contains the edges of the hypergraph which are subsets of Vi. We show that there exists no online hypergraph coloring algorithm with sublinear competitive ratio. Furthermore we investigate some particular classes of hypergraphs (k-uniform hypergraphs, hypergraphs with bounded matching number, projective planes), we analyse the online algorithm FF and give matching lower bounds for these classes.     

Automatic online news monitoring and classification for syndromic surveillance

Syndromic surveillance can play an important role in protecting the public's health against infectious diseases. Infectious disease outbreaks can have a devastating effect on society as well as the economy, and global awareness is therefore critical to protecting against major outbreaks. By monitoring online news sources and developing an accurate news classification system for syndromic surveillance, public health personnel can be apprised of outbreaks and potential outbreak situations. In this study, we have developed a framework for automatic online news monitoring and classification for syndromic surveillance. The framework is unique and none of the techniques adopted in this study have been previously used in the context of syndromic surveillance on infectious diseases. In recent classification experiments, we compared the performance of different feature subsets on different machine learning algorithms. The results showed that the combined feature subsets including Bag of Words, Noun Phrases, and Named Entities features outperformed the Bag of Words feature subsets. Furthermore, feature selection improved the performance of feature subsets in online news classification. The highest classification performance was achieved when using SVM upon the selected combination feature subset.     

The Worst Page-Replacement Policy

In this paper, we consider the following question: what is the worst possible page-replacement strategy? Our goal is to devise an online strategy that has the highest possible fraction of page faults as compared to the worst offline strategy. We show that there is no deterministic, online page-replacement strategy that is competitive with the worst offline strategy. We give a randomized strategy based on the “most-recently-used” heuristic and show that this strategy is the worst possible online page-replacement strategy.     

A note on the online First-Fit algorithm for coloring k-inductive graphs

In a FOCS 1990 paper, S. Irani proved that the First-Fit online algorithm for coloring a graph uses at most O(klogn) colors for k-inductive graphs. In this note we provide a very short proof of this fact.     

Online knapsack with resource augmentation

It is known that online knapsack is not competitive. This negative result remains true even if items are removable. In this paper we consider online removable knapsack with resource augmentation, in which we hold a knapsack of capacity R?1 and aim at maintaining a feasible packing to maximize the total profit of items packed into the knapsack. Both scenarios that removal of accepted items is allowed and is not allowed are investigated. We evaluate an online algorithm by comparing the resulting packing to an optimal packing that uses a knapsack of capacity one. Optimal online algorithms are derived for both the weighted case (items have arbitrary profits) and the unweighted case (the profit of an item is equal to its size).     

Scheduling parallel jobs to minimize the makespan

We consider the NP-hard problem of scheduling parallel jobs with release dates on identical parallel machines to minimize the makespan. A parallel job requires simultaneously a prespecified, job-dependent number of machines when being processed. We prove that the makespan of any nonpreemptive list-schedule is within a factor of 2 of the optimal preemptive makespan. This gives the best-known approximation algorithms for both the preemptive and the nonpreemptive variant of the problem. We also show that no list-scheduling algorithm can achieve a better performance guarantee than 2 for the nonpreemptive problem, no matter which priority list is chosen. List-scheduling also works in the online setting where jobs arrive over time and the length of a job becomes known only when it completes; it therefore yields a deterministic online algorithm with competitive ratio 2 as well. In addition, we consider a different online model in which jobs arrive one by one and need to be scheduled before the next job becomes known. We show that no list-scheduling algorithm has a constant competitive ratio. Still, we present the first online algorithm for scheduling parallel jobs with a constant competitive ratio in this context. We also prove a new information-theoretic lower bound of 2.25 for the competitive ratio of any deterministic online algorithm for this model. Moreover, we show that 6/5 is a lower bound for the competitive ratio of any deterministic online algorithm of the preemptive version of the model jobs arriving over time.     

Online chasing problems for regular polygons

We consider a server location problem with only one server to move. In this paper we assume that a request is given as a region and that the service can be done anywhere inside the region. Namely, for each request an online algorithm chooses an arbitrary point in the region and moves the server there. Note that if every request is a single point and the server must exactly go there in the given order as conventional server problems, there is no choice for the online player and the problem is trivial. Our main result shows that if the region is a regular n-gon, the competitive ratio of the greedy algorithm is for odd n, and for even n. In particular for a square region, the greedy algorithm turns out to be optimal.     

Improved analysis of the greedy algorithm for stochastic matching

The stochastic matching problem with applications in online dating and kidney exchange was introduced by Chen et al. (2009) [1] together with a simple greedy strategy. They proved it is a 4-approximation, but conjectured that the greedy algorithm is in fact a 2-approximation. In this paper we confirm this hypothesis.     

Creating a consensus ranking of proposals from reviewers’ partial ordinal rankings

Peer review of research proposals and articles is an essential element in R&D processes worldwide. In most cases, each reviewer evaluates a small subset of the candidate proposals. The review board is then faced with the challenge of creating an overall “consensus” ranking on the basis of many partial rankings. In this paper we propose a branch-and-bound model to support the construction of an aggregate ranking from the partial rankings provided by the reviewers. In a recent paper we proposed ways to allocate proposals to reviewers so as to achieve the maximum possible overlap among the subsets of proposals allocated to different reviewers. Here, we develop a special branch-and-bound algorithm that utilizes the overlap generated through our earlier methods to enable discrimination in ranking the competing proposals. The effectiveness and efficiency of the algorithm is demonstrated with small numerical examples and tested through an extensive simulation experiment.     

Improving nearest neighbor classification using Ensembles of Evolutionary Generated Prototype Subsets

One of the most accurate types of prototype selection algorithms, preprocessing techniques that select a subset of instances from the data before applying nearest neighbor classification to it, are evolutionary approaches. These algorithms result in very high accuracy and reduction rates, but unfortunately come at a substantial computational cost. In this paper, we introduce a framework that allows to efficiently use the intermediary results of the prototype selection algorithms to further increase their accuracy performance. Instead of only using the fittest prototype subset generated by the evolutionary algorithm, we use multiple prototype subsets in an ensemble setting. Secondly, in order to classify a test instance, we only use prototype subsets that accurately classify training instances in the neighborhood of that test instance. In an experimental evaluation, we apply our new framework to four state-of-the-art prototype selection algorithms and show that, by using our framework, more accurate results are obtained after less evaluations of the prototype selection method. We also present a case study with a prototype generation algorithm, showing that our framework is easily extended to other preprocessing paradigms as well.     

Optimally competitive list batching

Batching has been studied extensively in the offline case, but applications such as manufacturing or TCP acknowledgment often require online solutions.We consider online batching problems, where the order of jobs to be batched is fixed and where we seek to minimize the sum of the completion times of the jobs. We present optimally competitive online algorithms for both s-batch and p-batch problems, and we also derive results for certain naturally occurring special cases, such as the case of unit processing times.     

Scheduling on two identical machines with a speed-up resource

We address a variant of scheduling problem on two identical machines, where we are given an additional speed-up resource. If a job uses the resource, its processing time may decrease. However, at any time the resource can only be used by at most one job. The objective is to minimize the makespan. For the offline version, we present an FPTAS. For the online version where jobs arrive over list, we propose an online algorithm with competitive ratio of 1.781, and show a lower bound of 1.686 for any online algorithm.     

A general framework for computing maximal contractions

This paper investigates the problem of computing all maximal contractions of a given formula set Γ with respect to a consistent set Δ of atomic formulas and negations of atomic formulas. We first give a constructive definition of minimal inconsistent subsets and propose an algorithmic framework for computing all minimal inconsistent subsets of any given formula set. Then we present an algorithm to compute all maximal contractions fromminimal inconsistent subsets. Based on the algorithmic framework and the algorithm, we propose a general framework for computing all maximal contractions. The computability of the minimal inconsistent subset and maximal contraction problems are discussed. Finally, we demonstrate the ability of this framework by applying it to the first-order language without variables and design an algorithmfor the computation of all maximal contractions.     

The orthogonal CNN problem

The online CNN problem had no known competitive algorithms for a long time. Sitters, Stougie and de Paepe showed that there exists a competitive online algorithm for this problem. However, both their algorithm and analysis are quite complicated, and above all, their upper bound for the competitive ratio is 10⁵. In this paper, we examine why this problem seems so difficult. To this end we introduce a nontrivial restriction, orthogonality, against this problem and show that it decreases the competitive ratio dramatically, down to at most 9.     

A simpler competitive analysis for scheduling equal-length jobs on one machine with restarts

We consider the online problem of scheduling jobs with equal processing times on a single machine. Each job has a release time and a deadline, and the goal is to maximize the number of jobs completed by their deadlines. Chrobak et al. (2007, SICOMP 36:6) introduce a preempt-restart model in which progress toward completing a preempted job is lost, yet that job can be restarted from scratch. They provide a -competitive deterministic algorithm and show that this is the optimal competitiveness. Their analysis is based on a complex charging scheme among individual jobs and the use of several partial functions and mappings for assigning the charges. In this paper, we provide an alternative proof of the result using a more global potential argument to compare the relative progress of the algorithm versus the optimal schedule over time. This new proof is significantly simpler and more intuitive that the original, and our technique is applicable to related problems.     

New Bounds for Multidimensional Packing

Abstract. New upper and lower bounds are presented for a multidimensional generalization of bin packing called box packing. Several variants of this problem, including bounded space box packing, square packing, variable-sized box packing and resource augmented box packing are also studied. The main results, stated for d=2 , are as follows: a new upper bound of 2.66013 for online box packing, a new 14/9 + ɛ polynomial time offline approximation algorithm for square packing, a new upper bound of 2.43828 for online square packing, a new lower bound of 1.62176 for online square packing, a new lower bound of 2.28229 for bounded space online square packing and a new upper bound of 2.32571 for online two-sized box packing.     

Model-based evaluation of clustering validation measures

A cluster operator takes a set of data points and partitions the points into clusters (subsets). As with any scientific model, the scientific content of a cluster operator lies in its ability to predict results. This ability is measured by its error rate relative to cluster formation. To estimate the error of a cluster operator, a sample of point sets is generated, the algorithm is applied to each point set and the clusters evaluated relative to the known partition according to the distributions, and then the errors are averaged over the point sets composing the sample. Many validity measures have been proposed for evaluating clustering results based on a single realization of the random-point-set process. In this paper we consider a number of proposed validity measures and we examine how well they correlate with error rates across a number of clustering algorithms and random-point-set models. Validity measures fall broadly into three classes: internal validation is based on calculating properties of the resulting clusters; relative validation is based on comparisons of partitions generated by the same algorithm with different parameters or different subsets of the data; and external validation compares the partition generated by the clustering algorithm and a given partition of the data. To quantify the degree of similarity between the validation indices and the clustering errors, we use Kendall's rank correlation between their values. Our results indicate that, overall, the performance of validity indices is highly variable. For complex models or when a clustering algorithm yields complex clusters, both the internal and relative indices fail to predict the error of the algorithm. Some external indices appear to perform well, whereas others do not. We conclude that one should not put much faith in a validity score unless there is evidence, either in terms of sufficient data for model estimation or prior model knowledge, that a validity measure is well-correlated to the error rate of the clustering algorithm.     

An improved algorithm for online coloring of intervals with bandwidth

We present an improved online algorithm for coloring interval graphs with bandwidth. This problem has recently been studied by Adamy and Erlebach and a 195-competitive online strategy has been presented. We improve this by presenting a 10-competitive strategy. To achieve this result, we use variants of an optimal online coloring algorithm due to Kierstead and Trotter.