33876850
Subquadratic Algorithms for Workload-Aware Haar Wavelet Synopses
Given a signal A of N dimensions, the problem is to obtain a representation R for it that is a linear combination of vectors in the dictionary H of Haar wavelets. The quality of the representation R is determined by B, the number of vectors from H used, and δ, the error between R and A. Traditionally, δ has been the sum squared error e R=∑i (R[i]–A[i])2, in which case, Parseval's theorem from 1799 helps solve the problem of finding the R with smallest eR in O(N) time. 
 
Recently, motivated by database applications, researchers have sought other notions of error such as workload-aware error, or $\epsilon_{{\mathbf R}}^{\pi}=\sum_i \pi[i] ({\mathbf R}[i]-{\mathbf A}[i])^2$, where π[i] is the workload or the weight for i, and 
 
maximum pointwise absolute error, eg., $\epsilon_{{\mathbf R}}^{\infty}=\max_i |{\mathbf R}[i]-{\mathbf A}[i]|$. 
 
Recent results give Ω(N2) time algorithms for finding R that minimize these errors. 
 
We present subquadratic algorithms for versions of these problems. We present a near-linear time algorithm to minimize e Rπ when π is compressible. To minimize e R∞, we give an O(N2−− e) time algorithm. These algorithms follow a natural dynamic programming approach developed recently, but the improvements come from exploiting local structural properties of the Haar wavelet representations of signals we identify. 
 
Sparse approximation theory is a mature area of Mathematics that has traditionally studied signal representations with Haar wavelets. It is interesting that the past few years have seen new problems in this area motivated by Computer Science concerns: we pose a few new additional problems and some partial results.
11291209
Randomization in Parallel Stringology
In this abstract, we provide an overview of our survey of randomized techniques for exploiting the parallelism in string matching problems. Broadly, the study of string matching falls into two categories: standard stringology and nonstandard stringology. Standard Stringology concerns the study of various exact matching problems. The fundamental problem here is the basic string matching problem where given a pattern string p 2 m and a text string t 2 n, the problem is to nd all occurrences i in t where the pattern occurs, that is, t[i i+m 1] = p[1 m]. Other well-studied problems within standard stringology include multiple pattern matching, dictionary matching, text indexing, etc. Non-standard Stringology concerns the study of various inexact matching problems. A fundamental problem here is string matching with wildcards where the problem, as before, is to nd all occurrences of the pattern within the text; however, some positions in the text and the pattern are marked as \wildcards"(denoted ), that is, these positions match whatever be the symbol in the string they align against. Formally, given p occurs in t at i if for all 1 j m, t[i+j 1] = p[j] if p[j] 6= and t[i+j 1] 6= . Another important problem here is the k-mismatches problem in which the goal is to determine all those positions in the text where the pattern occurs with at most k mismatches amongst the aligned symbols. Other problems here include subset matching, range matching etc. Stringology includes study of many other problems involving
1714371
Bidding to the Top: VCG and Equilibria of Position-Based Auctions
Many popular search engines run an auction to determine the placement of advertisements next to search results. Current auctions at Google and Yahoo! let advertisers specify a single amount as their bid in the auction. This bid is interpreted as the maximum amount the advertiser is willing to pay per click on its ad. When search queries arrive, the bids are used to rank the ads linearly on the search result page. Advertisers seek to be high on the list, as this attracts more attention and more clicks. The advertisers pay for each user who clicks on their ad, and the amount charged depends on the bids of all the advertisers participating in the auction. 
 
We study the problem of ranking ads and associated pricing mechanisms when the advertisers not only specify a bid, but additionally express their preference for positions in the list of ads. In particular, we study prefix position auctions where advertiser i can specify that she is interested only in the top κi positions. 
 
We present a simple allocation and pricing mechanism that generalizes the desirable properties of current auctions that do not have position constraints. In addition, we show that our auction has an envy-free [1] or symmetric [2] Nash equilibrium with the same outcome in allocation and pricing as the well-known truthful Vickrey-Clarke-Groves (VCG) auction. Furthermore, we show that this equilibrium is the best such equilibrium for the advertisers in terms of the profit made by each advertiser. We also discuss other position-based auctions.
622090
Detecting False Matches in String-Matching Algorithms
Abstract. Consider a text string of length n, a pattern string of length m, and a match vector of length n which declares each location in the text to be either a mismatch (the pattern does not occur beginning at that location in the text) or a potential match (the pattern may occur beginning at that location in the text). Some of the potential matches could be false, i.e., the pattern may not occur beginning at some location in the text declared to be a potential match. We investigate the complexity of two problems in this context, namely, checking if there is any false match, and identifying all the false matches in the match vector. We present an algorithm on the CRCW PRAM that checks if there exists a false match in O(1) time using O(n) processors. This algorithm does not require preprocessing the pattern. Therefore, checking for false matches is provably simpler than string matching since string matching takes 
 $\Omega(\log\log m)$ time on the CRCW PRAM. We use this simple algorithm to convert the Karp—Rabin Monte Carlo type string-matching algorithm into a Las Vegas type algorithm without asymptotic loss in complexity. We also present an efficient algorithm for identifying all the false matches and, as a consequence, show that string-matching algorithms take 
 $\Omega(\log\log m)$ time even given the flexibility to output a few false matches.
2478393
Compressing and searching XML data via two zips
XML is fast becoming the standard format to store, exchange and publish over the web, and is getting embedded in applications. Two challenges in handling XML are its size (the XML representation of a document is significantly larger than its native state) and the complexity of its search (XML search involves path and content searches on labeled tree structures). We address the basic problems of compression, navigation and searching of XML documents. In particular, we adopt recently proposed theoretical algorithms [11] for succinct tree representations to design and implement a compressed index for XML, called XBZIPiNDEX, in which the XML document is maintained in a highly compressed format, and both navigation and searching can be done uncompressing only a tiny fraction of the data. This solution relies on compressing and indexing two arrays derived from the XML data. With detailed experiments we compare this with other compressed XML indexing and searching engines to show that XBZIPiNDEX has compression ratio up to 35% better than the ones achievable by those other tools, and its time performance on some path and content search operations is order of magnitudes faster: few milliseconds over hundreds of MBs of XML files versus tens of seconds, on standard XML data sources.
16380650
The Graham-Knowlton Problem Revisited
AbstractIn the late 60s Graham and Knowlton introduced the WIP (wire
identification problem) that affected electricians: match the wires in
the ceiling to those in the basement while making the fewest trips. We
revisit this problem and study its variants and generalizations; we
provide a combinatorial characterization of the solution(s) in terms of
an associated hypergraph and obtain nearly tight bounds on the minimum
number of trips.
14958117
Computational identification of novel chitinase-like proteins in the Drosophila melanogaster genome
MOTIVATION
Multiple chitinases as well as lectins closely related to them have been characterized previously from many insect species and the corresponding genes/cDNAs have been cloned. However, the identification of the entire assortment of genes for chitinase family proteins and their differences in biochemical properties have not been carried out in any individual insect species. The completion of the entire DNA sequence of Drosophila melanogaster (fruit fly) genome and identification of open reading frames presents an opportunity to study the structures and functions of chitinase-like proteins, and also to identify new members of this family in Drosophila. We are, therefore, interested in studying the functional genomics of chitinase-like gene families in insects.


METHODS
We searched the Drosophila protein sequences database using fully characterized insect chitinase sequences and BLASTP software, identified all the putative chitinase-like proteins encoded in Drosophila genome, and predicted their structures using domain analysis tools. A phylogenetic analysis of the chitinase-like proteins from Drosophila and several other insect species was carried out. The structures of these chitinases were modeled using homology modeling software.


RESULTS
Our analysis revealed the presence of 18 chitinase-like proteins in the Drosophila protein database. Among these are seven novel chitinase-like proteins that contain four signature amino acid sequences of chitinases belonging to family 18 glycosylhydrolases, including both acidic and hydrophobic amino acid residues critical for enzyme activity. All the proteins contain at least one catalytic domain with one having four catalytic domains. Phylogenetic analysis of chitinase-like proteins from Drosophila and other insects revealed an evolutionary relationship among all these proteins, which indicated gene duplication and domain shuffling to generate the observed diversity in the encoded proteins. Homology modeling showed that all the Drosophila chitinase-like proteins contain one or more catalytic domains with a (alpha/beta)8 barrel-like structure. Our results suggest that insects utilize multiple family 18 chitinolytic enzymes and also non-enzymatic chitinase-like proteins for degrading/remodeling/binding to chitin in different insect anatomical extracellular structures, such as the cuticle, peritrophic membrane, trachea and mouth parts during insect development, and possibly for other roles including chitin synthesis.


AVAILABILITY
Perl program and supplementary material are available at http://www.ksu.edu/bioinformatics/supplementary.htm