Optimally Adaptive Integration of Univariate Lipschitz Functions

We consider the problem of approximately integrating a Lipschitz function f (with a known Lipschitz constant) over an interval. The goal is to achieve an additive error of at most ε using as few samples of f as possible. We use the adaptive framework: on all problem instances an adaptive algorithm should perform almost as well as the best possible algorithm tuned for the particular problem instance. We distinguish between and , the performances of the best possible deterministic and randomized algorithms, respectively. We give a deterministic algorithm that uses samples and show that an asymptotically better algorithm is impossible. However, any deterministic algorithm requires samples on some problem instance. By combining a deterministic adaptive algorithm and Monte Carlo sampling with variance reduction, we give an algorithm that uses at most samples. We also show that any algorithm requires samples in expectation on some problem instance (f,ε), which proves that our algorithm is optimal.     

Path Hitting in Acyclic Graphs

An instance of the path hitting problem consists of two families of paths, and ℋ, in a common undirected graph, where each path in ℋ is associated with a non-negative cost. We refer to and ℋ as the sets of demand and hitting paths, respectively. When p∈ℋ and share at least one mutual edge, we say that p hits q. The objective is to find a minimum cost subset of ℋ whose members collectively hit those of . In this paper we provide constant factor approximation algorithms for path hitting, confined to instances in which the underlying graph is a tree, a spider, or a star. Although such restricted settings may appear to be very simple, we demonstrate that they still capture some of the most basic covering problems in graphs. Our approach combines several novel ideas: We extend the algorithm of Garg, Vazirani and Yannakakis (Algorithmica, 18:3–20, 1997) for approximate multicuts and multicommodity flows in trees to prove new integrality properties; we present a reduction that involves multiple calls to this extended algorithm; and we introduce a polynomial-time solvable variant of the edge cover problem, which may be of independent interest. An extended abstract of this paper appeared in Proceedings of the 14th Annual European Symposium on Algorithms, 2006. This work is part of D. Segev’s Ph.D. thesis prepared at Tel-Aviv University under the supervision of Prof. Refael Hassin.     

Measuring ranked list robustness for query performance prediction

We introduce the notion of ranking robustness, which refers to a property of a ranked list of documents that indicates how stable the ranking is in the presence of uncertainty in the ranked documents. We propose a statistical measure called the robustness score to quantify this notion. Our initial motivation for measuring ranking robustness is to predict topic difficulty for content-based queries in the ad-hoc retrieval task. Our results demonstrate that the robustness score is positively and consistently correlation with average precision of content-based queries across a variety of TREC test collections. Though our focus is on prediction under the ad-hoc retrieval task, we observe an interesting negative correlation with query performance when our technique is applied to named-page finding queries, which are a fundamentally different kind of queries. A side effect of this different behavior of the robustness score between the two types of queries is that the robustness score is also found to be a good feature for query classification.      

A scalable algorithm for mining maximal frequent sequences using a sample

In this paper, we propose an efficient scalable algorithm for mining Maximal Sequential Patterns using Sampling (MSPS). The MSPS algorithm reduces much more search space than other algorithms because both the subsequence infrequency-based pruning and the supersequence frequency-based pruning are applied. In MSPS, a sampling technique is used to identify long frequent sequences earlier, instead of enumerating all their subsequences. We propose how to adjust the user-specified minimum support level for mining a sample of the database to achieve better overall performance. This method makes sampling more efficient when the minimum support is small. A signature-based method and a hash-based method are developed for the subsequence infrequency-based pruning when the seed set of frequent sequences for the candidate generation is too big to be loaded into memory. A prefix tree structure is developed to count the candidate sequences of different sizes during the database scanning, and it also facilitates the customer sequence trimming. Our experiments showed MSPS has very good performance and better scalability than other algorithms. Congnan Luo received the B.E. degree in Computer Science from Tsinghua University, Beijing, P.R. China, in 1997, the M.S. degree in Computer Science from the Institute of Software, Chinese Academy of Sciences, Beijing, P.R. China, in 2000, and the Ph.D. degree in Computer Science and Engineering from Wright State University, Dayton, OH, in 2006. Currently he is a technical staff at the Teradata division of NCR in San Diego, CA, and his research interests include data mining, machine learning, and databases. Soon M. Chung received the B.S. degree in Electronic Engineering from Seoul National University, Korea, in 1979, the M.S. degree in Electrical Engineering from Korea Advanced Institute of Science and Technology, Korea, in 1981, and the Ph.D. degree in Computer Engineering from Syracuse University, Syracuse, New York, in 1990. He is currently a Professor in the Department of Computer Science and Engineering at Wright State University, Dayton, OH. His research interests include database, data mining, Grid computing, text mining, XML, and parallel and distributed processing.     

A survey on algorithms for mining frequent itemsets over data streams

The increasing prominence of data streams arising in a wide range of advanced applications such as fraud detection and trend learning has led to the study of online mining of frequent itemsets (FIs). Unlike mining static databases, mining data streams poses many new challenges. In addition to the one-scan nature, the unbounded memory requirement and the high data arrival rate of data streams, the combinatorial explosion of itemsets exacerbates the mining task. The high complexity of the FI mining problem hinders the application of the stream mining techniques. We recognize that a critical review of existing techniques is needed in order to design and develop efficient mining algorithms and data structures that are able to match the processing rate of the mining with the high arrival rate of data streams. Within a unifying set of notations and terminologies, we describe in this paper the efforts and main techniques for mining data streams and present a comprehensive survey of a number of the state-of-the-art algorithms on mining frequent itemsets over data streams. We classify the stream-mining techniques into two categories based on the window model that they adopt in order to provide insights into how and why the techniques are useful. Then, we further analyze the algorithms according to whether they are exact or approximate and, for approximate approaches, whether they are false-positive or false-negative. We also discuss various interesting issues, including the merits and limitations in existing research and substantive areas for future research.     

Non-negative matrix factorization for semi-supervised data clustering

Traditional clustering algorithms are inapplicable to many real-world problems where limited knowledge from domain experts is available. Incorporating the domain knowledge can guide a clustering algorithm, consequently improving the quality of clustering. In this paper, we propose SS-NMF: a semi-supervised non-negative matrix factorization framework for data clustering. In SS-NMF, users are able to provide supervision for clustering in terms of pairwise constraints on a few data objects specifying whether they “must” or “cannot” be clustered together. Through an iterative algorithm, we perform symmetric tri-factorization of the data similarity matrix to infer the clusters. Theoretically, we show the correctness and convergence of SS-NMF. Moveover, we show that SS-NMF provides a general framework for semi-supervised clustering. Existing approaches can be considered as special cases of it. Through extensive experiments conducted on publicly available datasets, we demonstrate the superior performance of SS-NMF for clustering.

Fixed-Parameter Complexity of Minimum Profile Problems

The profile of a graph is an integer-valued parameter defined via vertex orderings; it is known that the profile of a graph equals the smallest number of edges of an interval supergraph. Since computing the profile of a graph is an NP-hard problem, we consider parameterized versions of the problem. Namely, we study the problem of deciding whether the profile of a connected graph of order n is at most n−1+k, considering k as the parameter; this is a parameterization above guaranteed value, since n−1 is a tight lower bound for the profile. We present two fixed-parameter algorithms for this problem. The first algorithm is based on a forbidden subgraph characterization of interval graphs. The second algorithm is based on two simple kernelization rules which allow us to produce a kernel with linear number of vertices and edges. For showing the correctness of the second algorithm we need to establish structural properties of graphs with small profile which are of independent interest. A preliminary version of the paper is published in Proc. IWPEC 2006, LNCS vol. 4169, 60–71.     

An Improved (and Practical) Parameterized Algorithm for the Individual Haplotyping Problem MFR with Mate-Pairs

The Individual Haplotyping MFR problem is a computational problem that, given a set of DNA sequence fragment data of an individual, induces the corresponding haplotypes by dropping the minimum number of fragments. Bafna, Istrail, Lancia, and Rizzi proposed an algorithm of time O(2^2k m ² n+2^3k m ³) for the problem, where m is the number of fragments, n is the number of SNP sites, and k is the maximum number of holes in a fragment. When there are mate-pairs in the input data, the parameter k can be as large as 100, which would make the Bafna-Istrail-Lancia-Rizzi algorithm impracticable. The current paper introduces a new algorithm PM-MFR of running time , where k ₁ is the maximum number of SNP sites that a fragment covers (k ₁ is smaller than n), and k ₂ is the maximum number of fragments that cover a SNP site (k ₂ is usually about 10). Since the time complexity of the algorithm PM-MFR is not directly related to the parameter k, the algorithm solves the Individual Haplotyping MFR problem with mate-pairs more efficiently and is more practical in real biological applications. This research was supported in part by the National Natural Science Foundation of China under Grant Nos. 60433020 and 60773111, the Program for New Century Excellent Talents in University No. NCET-05-0683, the Program for Changjiang Scholars and Innovative Research Team in University No. IRT0661, and the Scientific Research Fund of Hunan Provincial Education Department under Grant No. 06C526.     

Grouping Techniques for Scheduling Problems: Simpler and Faster

In this paper we describe a general grouping technique to devise faster and simpler approximation schemes for several scheduling problems. We illustrate the technique on two different scheduling problems: scheduling on unrelated parallel machines with costs and the job shop scheduling problem. The time complexity of the resulting approximation schemes is always linear in the number n of jobs, and the multiplicative constant hidden in the O(n) running time is reasonably small and independent of the error ε. Supported by Swiss National Science Foundation project 200020-109854, “Approximation Algorithms for Machine scheduling Through Theory and Experiments II”. A preliminary version of this paper appeared in the Proceedings of ESA’01.     

A hybrid aggregation and compression technique for road network databases

Vector data and in particular road networks are being queried, hosted and processed in many application domains such as in mobile computing. Many client systems such as PDAs would prefer to receive the query results in unrasterized format without introducing an overhead on overall system performance and result size. While several general vector data compression schemes have been studied by different communities, we propose a novel approach in vector data compression which is easily integrated within a geospatial query processing system. It uses line aggregation to reduce the number of relevant tuples and Huffman compression to achieve a multi-resolution compressed representation of a road network database. Our experiments performed on an end-to-end prototype verify that our approach exhibits fast query processing on both client and server sides as well as high compression ratio.