On the Complexity of Exact Pattern Matching in Graphs: Binary Strings and Bounded Degree

Exact pattern matching in labeled graphs is the problem of searching paths of a graph $G=(V,E)$ that spell the same string as the pattern $P[1..m]$. This basic problem can be found at the heart of more complex operations on variation graphs in computational biology, of query operations in graph databases, and of analysis operations in heterogeneous networks, where the nodes of some paths must match a sequence of labels or types. We describe a simple conditional lower bound that, for any constant $\epsilon>0$, an $O(|E|^{1 - \epsilon} \, m)$-time or an $O(|E| \, m^{1 - \epsilon})$-time algorithm for exact pattern matching on graphs, with node labels and patterns drawn from a binary alphabet, cannot be achieved unless the Strong Exponential Time Hypothesis (SETH) is false. The result holds even if restricted to undirected graphs of maximum degree three or directed acyclic graphs of maximum sum of indegree and outdegree three. Although a conditional lower bound of this kind can be somehow derived from previous results (Backurs and Indyk, FOCS'16), we give a direct reduction from SETH for dissemination purposes, as the result might interest researchers from several areas, such as computational biology, graph database, and graph mining, as mentioned before. Indeed, as approximate pattern matching on graphs can be solved in $O(|E|\,m)$ time, exact and approximate matching are thus equally hard (quadratic time) on graphs under the SETH assumption. In comparison, the same problems restricted to strings have linear time vs quadratic time solutions, respectively, where the latter ones have a matching SETH lower bound on computing the edit distance of two strings (Backurs and Indyk, STOC'15).Comment: Using Lemma 12 and Lemma 13 might to be enough to prove Lemma 14. However, the proof of Lemma 14 is correct if you assume that the graph used in the reduction is a DAG. Hence, since the problem is already quadratic for a DAG and a binary alphabet, it has to be quadratic also for a general graph and a binary alphabe

Term-Specific Eigenvector-Centrality in Multi-Relation Networks

Fuzzy matching and ranking are two information retrieval techniques widely used in web search. Their application to structured data, however, remains an open problem. This article investigates how eigenvector-centrality can be used for approximate matching in multi-relation graphs, that is, graphs where connections of many different types may exist. Based on an extension of the PageRank matrix, eigenvectors representing the distribution of a term after propagating term weights between related data items are computed. The result is an index which takes the document structure into account and can be used with standard document retrieval techniques. As the scheme takes the shape of an index transformation, all necessary calculations are performed during index tim

WAQS : a web-based approximate query system

The Web is often viewed as a gigantic database holding vast stores of information and provides ubiquitous accessibility to end-users. Since its inception, the Internet has experienced explosive growth both in the number of users and the amount of content available on it. However, searching for information on the Web has become increasingly difficult. Although query languages have long been part of database management systems, the standard query language being the Structural Query Language is not suitable for the Web content retrieval. In this dissertation, a new technique for document retrieval on the Web is presented. This technique is designed to allow a detailed retrieval and hence reduce the amount of matches returned by typical search engines. The main objective of this technique is to allow the query to be based on not just keywords but also the location of the keywords within the logical structure of a document. In addition, the technique also provides approximate search capabilities based on the notion of Distance and Variable Length Don\u27t Cares. The proposed techniques have been implemented in a system, called Web-Based Approximate Query System, which contains an SQL-like query language called Web-Based Approximate Query Language. Web-Based Approximate Query Language has also been integrated with EnviroDaemon, an environmental domain specific search engine. It provides EnviroDaemon with more detailed searching capabilities than just keyword-based search. Implementation details, technical results and future work are presented in this dissertation

On the Complexity of String Matching for Graphs

Peer reviewe

Ala- ja ylärajoja merkkijonon etsinnälle verkosta

String Matching in Labelled Graphs (SMLG) is a generalisation of the classic problem of finding a match for a string into a text. In SMLG, we are given a pattern string and a graph with node labels, and we want to find a path whose node labels match the pattern string. This problem has been studied since 1992, and it was initially intended to model the problem of finding a link in a hypertext. Recently, the problem received attention due to its applications in bioinformatics, but all of the solutions, old and new, failed to run in truly sub-quadratic time. In this work, based on four published papers, we study SMLG from different angles, first proving conditional lower bounds, and then proposing efficient algorithms for special classes of graphs. In the first paper, we unveil the reason behind the hardness of SMLG, showing a quadratic conditional lower bound based on the Orthogonal Vectors Hypothesis and the Strong Exponential Time Hypothesis. The techniques that we employ come from the fine-grained complexity, and involve finding linear-time reductions from the Orthogonal Vectors problem to different variations of SMLG. In the second paper, we strengthen our findings by showing that an indexing data structure built in polynomial time is not enough to provide subquadratic time queries for SMLG. We devise a general framework for obtaining indexing lower bounds out of regular lower bounds, and we prove the indexing lower bound for SMLG as an application of this technique. In the third paper, we surpass the limitations of our lower bounds by identifying a class of graphs, called founder block graphs, which support linear time queries after subquadratic indexing. This class of graph effectively represents collections of strings called multiple sequence alignments, if gap characters are not present. In the fourth paper, we significantly improve our previous results on efficiently indexable graphs. We propose elastic founder graphs, a superset of founder block graphs, that are able to represent multiple sequence alignments with gaps. Moreover, we propose algorithms for constructing elastic founder graph, indexing them, and perform queries in linear time.Merkkijonon etsintä verkosta (engl. String Matching in Labelled Graphs, SMLG) on yleistys klassiselle ongelmalle etsiä merkkijonohahmon osumaa tekstistä. SMLG ongelmassa syötteenä ovat merkkijonohahmo ja verkko, jonka solmuilla on merkkijonotunnisteet. Tavoitteena on löytää polku, jonka solmujen tunnisteet muodostavat tekstin, joka sisältää annetun merkkijonohahmon. Ongelmaa on tutkittu vuodesta 1992 alun alkaen mallintamaan linkkien etsintää hypertekstistä. Viime aikoina ongelma on tullut uudestaan esille bioinformatiikan saralla. Sekä vanhat että uudet ratkaisut eivät ole onnistuneet oleellisesti murtamaan neliöllistä aikavaativuutta ongelman ratkaisussa. Tässä työssä SMLG ongelmaa tarkastellaan eri näkökulmista perustuen neljään julkaisuun. Ensin todistetaan ehdollinen alaraja ongelman vaativuudelle. Sitten esitetään tehokkaita ratkaisuja erilaisille verkkojen aliluokille. Ensimmäisessä julkaisussa paljastamme syyn SMLG ongelman vaikeudelle johtamalla ehdollisen alarajan perustuen kohtisuorien vektorien hypoteesiin (engl. Orthogonal Vectors Hypothesis) ja vahvaan eksponentiaalisen aikavaativuuden hypoteesiin (engl. Strong Exponential Time Hypothesis). Tähän tulokseen käytämme hienorakenteisen vaativuusteorian (engl. fine-grained complexity) tekniikoita, kuten lineaariaikaista reduktiota kohtisuorien vektoreiden ongelmasta kohdeongelmaan, tässä tapauksessa eri variaatioille SMLG ongelmasta. Toisessa julkaisussa vahvistamme edellistä tulosta osoittamalla, että polynomiaikainen verkon indeksointi ei riitä tukemaan alle neliöaikaista merkkijonohahmon etsintää. Kehitämme yleisen kehikon tämän kaltaisten indeksointialarajojen johtamiseen tavallisista alarajoista, ja todistamme SMLG ongelman alarajan sovellutuksena tästä tekniikasta. Kolmannessa julkaisussa ohitamme alarajat identifioimalla verkkojen aliluokan, kantasegmentteihin perustuvat verkot (engl. founder block graphs), joilla indeksointi onnistuu alle neliöllisessä ajassa, jonka jälkeen merkkijonohahmon etsintää voidaan suorittaa lineaarisessa ajassa. Kantasegmentteihin perustuvilla verkoilla voidaan esittää merkkijonokokoelmien monilinjaukset, mikäli linjauksessa ei tarvita poistoja ja lisäyksiä. Neljännessä julkaisussa parannamme merkittävästi aiempia tuloksiamme indeksoitavista verkoista. Laajennamme kantasegmentteihin perustuvat verkot elastisuuden käsitteellä, jolloin ne voivat esittää mielivaltaisia monilinjauksia, joissa linjauksessa sallitaan poistot ja lisäykset. Tämän lisäksi johdamme algoritmeja näiden elastisten kantasegmentteihin perustuvien verkkojen muodostamiseen, indeksointiin, sekä merkkijonohahmojen etsintään

Wikis in Tuple Spaces

We consider storing the pages of a wiki in a tuple space and the effects this might have on the wiki experience. In particular, wiki pages are stored in tuples with a few identifying values such as title, author, revision date, content, etc. and pages are retrieved by sending the tuple space templates, such as one that gives the title but nothing else, leaving the tuple space to resolve to a single tuple. We use a tuple space wiki to avoid deadlocks, infinite loops, and wasted efforts when page edit contention arises and examine how a tuple space wiki changes the wiki experience.Comment: To appear at WMSCI 200