Taming computational complexity: efficient and parallel SimRank optimizations on undirected graphs

SimRank has been considered as one of the promising link-based ranking algorithms to evaluate similarities of web documents in many modern search engines. In this paper, we investigate the optimization problem of SimRank similarity computation on undirected web graphs. We first present a novel algorithm to estimate the SimRank between vertices in O(n3+ Kn2) time, where n is the number of vertices, and K is the number of iterations. In comparison, the most efficient implementation of SimRank algorithm in [1] takes O(K n3 ) time in the worst case. To efficiently handle large-scale computations, we also propose a parallel implementation of the SimRank algorithm on multiple processors. The experimental evaluations on both synthetic and real-life data sets demonstrate the better computational time and parallel efficiency of our proposed techniques

On the efficiency of estimating penetrating rank on large graphs

P-Rank (Penetrating Rank) has been suggested as a useful measure of structural similarity that takes account of both incoming and outgoing edges in ubiquitous networks. Existing work often utilizes memoization to compute P-Rank similarity in an iterative fashion, which requires cubic time in the worst case. Besides, previous methods mainly focus on the deterministic computation of P-Rank, but lack the probabilistic framework that scales well for large graphs. In this paper, we propose two efficient algorithms for computing P-Rank on large graphs. The first observation is that a large body of objects in a real graph usually share similar neighborhood structures. By merging such objects with an explicit low-rank factorization, we devise a deterministic algorithm to compute P-Rank in quadratic time. The second observation is that by converting the iterative form of P-Rank into a matrix power series form, we can leverage the random sampling approach to probabilistically compute P-Rank in linear time with provable accuracy guarantees. The empirical results on both real and synthetic datasets show that our approaches achieve high time efficiency with controlled error and outperform the baseline algorithms by at least one order of magnitude

Empirisch ernüchterte Phänomenologie des Leibes - über die Fissur in der phänomenologischen Psychologie

Im Laufe des 20. Jahrhunderts entstand innerhalb der europäischen Phänomenologie eine innovative und originelle Strömung namens Leib-Phänomenologie, Phénoménologie de la perception. Ihre grundsätzliche Kritik des Intellektualismus, Sensualismus und Objektivismus ist einer wissenschaftstheoretischen Inspiration der etablierten akademischen Psychologie dienlich. Hierbei besteht ihr inhaltlicher Fokus in der Analyse von Leibesphänomenen an der Schnittstelle von Körper und Geist. Während die traditionelle Psychologie hauptsächlich über diese Phänomene hinweggeht, generiert die Leib-Phänomenologie eine integrative Perspektive, um eine ganzheitliche Berücksichtigung der menschlichen Lebenswelt in der Psychologie zu ermöglichen. Die bisherigen Konzepte einer phänomenologischen Psychologie verweisen demgegenüber jedoch bisweilen ausschließlich auf die Methode der Phänomenologie, nicht auf die Perspektiven, mit denen die Leib-Phänomenologie die Psychologie bereichern kann.During the 20th century European phenomenology developed a genuine and innovative conceptual direction named Leib-Phänomenologie, Phénoménologie de la perception. It's fundamental critique of intellectualism, sensualism and objectivism offers an inventive standpoint of incitation for current academic psychology. In the course of this it's main focus are the originating experiences at the intersection of mind and body. Whereas traditional psychology mostly passes over these phenomena Leib-Phänomenologie recommends an integrative perspective to facilitate a holistic consideration of human experience. Recent concepts of a phenomenological psychology solely refer to the specific aspect of phenomenologies methodical critique of current psychology without obtaining the perspectives of Leib-Phänomenologie

Hatékony algoritmusok = Efficient algorithms

A kutatás során csoportunk egy sor új eredményt ért el a számítástudomány több területén. Ezek a területek: algebrai és szimbolikus számítások, számításelmélet, kombinatorikus optimalizálás, adatbázis-elmélet, adatbányászat és internetes algoritmusok. Néhány fontosabb eredmény: -- véges ponthalmazokhoz rendelhető Gröbner-bázisok és kapcsolódó struktúrák leírása kombinatorikai szempontból érdekes esetekben, -- a kvantumszámítások néhány fontos modelljének az összehasonlítása, számító erejük tisztázása, kvantumalgoritmusok kidolgozása, -- az ""Adatbázis-szerkezetek"" c. akadémiai Nívódíjas monográfia elkészülte, -- komoly előrelépést értünk el több, az interneten való kereséssel kapcsolatos kérdésben: új, hatékony algoritmusokat javasoltunk a világháló lapjainak személyes preferenciákat figyelembe vevő rangsorolására; algoritmust dolgoztunk ki a web spam jelenség nagy megbízhatóságú, automatikus detektálására; létrehoztunk egy kísérleti keresőrendszert, -- új hatékony adatbányászati algoritmusok kidolgozása és ezek alkalmazása; az alkalmazások közül kiemelkedik a telekommunikációs ügyfelek viselkedésének modellezésével kapcsolatos vizsgálatunk, amely Barabási Albert László világhírű kutatócsoportjával közös munka, és amelyről a The New York Times is beszámolt. | With the partial support of the present grant, we have achieved new results in several fields of computer science, including algebraic and symbolic computation, theoretical computer science, combinatorial optimization, database theory, data mining, algorithms for the internet. Some of the highlights are: -- a description of Gröbner bases and related structures attached to finite sets of of points, where the point sets have combinatorial significance, -- a comparison of some models of quantum computation from the perspective of computing power; development of new quantum algorithms, -- publication of the monograph ""Database structures"" (in Hungarian) which won the Quality Prize of the Akadémai Kiadó, -- significant advances in several directions connected to searching the internet: we proposed new, efficient methods for obtaining a personalized ranking of web pages; we proposed algorithms for the automatic and highly reliable detection of spam links in the web; we developed an experimental search engine, -- development and applications of new algorithms for several data mining tasks; among the applications the most important is a model for telecommunication customer behaviour, which has been elaborated in a joint project with the renowned group of Albert László Barabási, among others The York Times reported on some of our findings

Kombinatorikus optimalizálás alkalmazásai a villamosságtanban = Combinatorial optimization and its applications in electrical engineering

A kombinatorikus optimalizálás eszközeit (gráf- és matroidelméleti algoritmusok, bonyolultságelméleti vizsgálatok) alkalmaztuk villamosságtani és informatikai problémák megoldására, így konkrétan -- a nagybonyolultságú integrált áramkörök 2- és 3-dimenziós huzalozási kérdéseire (csatorna- vagy 'switchbox'-huzalozás, minimális összhosszúságú/területű/térfogatú huzalozás); -- hardware és software komponenseket egyaránt tartalmazó rendszerek szintézisére; -- távközlési hálózatok megbízhatóságának, szolgáltatás-minőségének növelésére; -- közlekedési hálózatok informatikai szolgáltatásaira (pl. haladó járművek adatai alapján a hálózat topológiájának vizsgálata, optimális útvonal javaslása); -- az adaptív elosztott multimédia szerver fejlesztésére; -- web oldalakon hatékonyabb kereső programmok készítésére. Eközben tiszta matematikai és számítástudományi eredményekhez is jutottunk, így konkrétan -- a gráfelméletben (összefüggőséget növelő kiegészítések, Hamilton-körök, gráf-izomorfia); -- a matroidelméletben (gyenge és erős leképezések); -- a kvantumszámításokban (periódikus függvények, rejtett részcsoportok); -- a paraméteres bonyolultságelméletben (gráfok és hipergráfok színezése és listaszínezése); -- rúdszerkezetek és ''tensegrity'' szerkezetek merevségének elméletében. | Methods of combinatorial optimization (algorithms for graphs and matroids, complexity considerations) were applied for various problems in electrical engineering and informatics, in particular -- for the detailed routing of 2- and 3-dimensional VLSI circuits (channel and switchbox routing, minimum length/area/volume routing); -- for hardware/software codesign; -- for improving the quality of service of telecommunication networks; -- for integrated traffic information services (e.g. map generation and route guidance from floating car data); -- for the developments of adaptive distributed multimedia servers; -- for designing more effective search algorithms in the web graph. During these studies we also obtained results in pure mathematics and in theoretical computer science as well, in particular -- in the theory of graphs (connectivity augmentations, Hamiltonian circuits, graph isomorphism); -- in the theory of matroids (strong and weak maps); -- in quantum computing (periodic functions, hidden subgroup properties); -- in parametrized complexity theory (colouring or list-colouring of graphs and hypergraphs); -- in the theory of rigidity of bar-and-joint and tensegrity frameworks

Dynamical SimRank search on time-varying networks

SimRank is an appealing pair-wise similarity measure based on graph structure. It iteratively follows the intuition that two nodes are assessed as similar if they are pointed to by similar nodes. Many real graphs are large, and links are constantly subject to minor changes. In this article, we study the efficient dynamical computation of all-pairs SimRanks on time-varying graphs. Existing methods for the dynamical SimRank computation [e.g., LTSF (Shao et al. in PVLDB 8(8):838–849, 2015) and READS (Zhang et al. in PVLDB 10(5):601–612, 2017)] mainly focus on top-k search with respect to a given query. For all-pairs dynamical SimRank search, Li et al.’s approach (Li et al. in EDBT, 2010) was proposed for this problem. It first factorizes the graph via a singular value decomposition (SVD) and then incrementally maintains such a factorization in response to link updates at the expense of exactness. As a result, all pairs of SimRanks are updated approximately, yielding (Formula presented.) time and (Formula presented.) memory in a graph with n nodes, where r is the target rank of the low-rank SVD. Our solution to the dynamical computation of SimRank comprises of five ingredients: (1) We first consider edge update that does not accompany new node insertions. We show that the SimRank update (Formula presented.) in response to every link update is expressible as a rank-one Sylvester matrix equation. This provides an incremental method requiring (Formula presented.) time and (Formula presented.) memory in the worst case to update (Formula presented.) pairs of similarities for K iterations. (2) To speed up the computation further, we propose a lossless pruning strategy that captures the “affected areas” of (Formula presented.) to eliminate unnecessary retrieval. This reduces the time of the incremental SimRank to (Formula presented.), where m is the number of edges in the old graph, and (Formula presented.) is the size of “affected areas” in (Formula presented.), and in practice, (Formula presented.). (3) We also consider edge updates that accompany node insertions, and categorize them into three cases, according to which end of the inserted edge is a new node. For each case, we devise an efficient incremental algorithm that can support new node insertions and accurately update the affected SimRanks. (4) We next study batch updates for dynamical SimRank computation, and design an efficient batch incremental method that handles “similar sink edges” simultaneously and eliminates redundant edge updates. (5) To achieve linear memory, we devise a memory-efficient strategy that dynamically updates all pairs of SimRanks column by column in just (Formula presented.) memory, without the need to store all (Formula presented.) pairs of old SimRank scores. Experimental studies on various datasets demonstrate that our solution substantially outperforms the existing incremental SimRank methods and is faster and more memory-efficient than its competitors on million-scale graphs

Time evolution of Wikipedia network ranking

We study the time evolution of ranking and spectral properties of the Google matrix of English Wikipedia hyperlink network during years 2003 - 2011. The statistical properties of ranking of Wikipedia articles via PageRank and CheiRank probabilities, as well as the matrix spectrum, are shown to be stabilized for 2007 - 2011. A special emphasis is done on ranking of Wikipedia personalities and universities. We show that PageRank selection is dominated by politicians while 2DRank, which combines PageRank and CheiRank, gives more accent on personalities of arts. The Wikipedia PageRank of universities recovers 80 percents of top universities of Shanghai ranking during the considered time period.Comment: 10 pages, 11 figures. Accepted for publication in EPJ

SimRank*: effective and scalable pairwise similarity search based on graph topology

Given a graph, how can we quantify similarity between two nodes in an effective and scalable way? SimRank is an attractive measure of pairwise similarity based on graph topologies. Its underpinning philosophy that “two nodes are similar if they are pointed to (have incoming edges) from similar nodes” can be regarded as an aggregation of similarities based on incoming paths. Despite its popularity in various applications (e.g., web search and social networks), SimRank has an undesirable trait, i.e., “zero-similarity”: it accommodates only the paths of equal length from a common “center” node, whereas a large portion of other paths are fully ignored. In this paper, we propose an effective and scalable similarity model, SimRank*, to remedy this problem. (1) We first provide a sufficient and necessary condition of the “zero-similarity” problem that exists in Jeh and Widom’s SimRank model, Li et al. ’s SimRank model, Random Walk with Restart (RWR), and ASCOS++. (2) We next present our treatment, SimRank*, which can resolve this issue while inheriting the merit of the simple SimRank philosophy. (3) We reduce the series form of SimRank* to a closed form, which looks simpler than SimRank but which enriches semantics without suffering from increased computational overhead. This leads to an iterative form of SimRank*, which requires O(Knm) time and O(n2) memory for computing all (n2) pairs of similarities on a graph of n nodes and m edges for K iterations. (4) To improve the computational time of SimRank* further, we leverage a novel clustering strategy via edge concentration. Due to its NP-hardness, we devise an efficient heuristic to speed up all-pairs SimRank* computation to O(Knm~) time, where m~ is generally much smaller than m. (5) To scale SimRank* on billion-edge graphs, we propose two memory-efficient single-source algorithms, i.e., ss-gSR* for geometric SimRank*, and ss-eSR* for exponential SimRank*, which can retrieve similarities between all n nodes and a given query on an as-needed basis. This significantly reduces the O(n2) memory of all-pairs search to either O(Kn+m~) for geometric SimRank*, or O(n+m~) for exponential SimRank*, without any loss of accuracy, where m~≪n2 . (6) We also compare SimRank* with another remedy of SimRank that adds self-loops on each node and demonstrate that SimRank* is more effective. (7) Using real and synthetic datasets, we empirically verify the richer semantics of SimRank*, and validate its high computational efficiency and scalability on large graphs with billions of edges

Az új algoritmusok és kódolási eljárások alkalmazása a mobil hírközlésben és informatikában = Application of new algorithms and coding procedures in mobile communications and computing

A kutatási munka során az alábbi résztémákban értünk el eredményeket: - mobil IP, - all IP hálózatok, - útkeresési algoritmusok, - hívásátadási algoritmusok, - mobil technológiák együttműködése, - a szolgáltatás minősége (QoS), - a mobil és informatikai hálózatok és rendszerek biztonsági kérdései, - több-felhasználós vétel, - kódosztásos többszörös hozzáférés, - forgalmi modellezés, - kódkonstrukció kódosztásos technológiákhoz, - kvantum számítástechnikai eljárások, - gráfelmélet, - kombinatorikus optimalizálás. A fenti szakterületeken végzett kutatásaink eredményei közül azokat emeljük ki, amelyeket az alábbi témákban értünk el: - A heterogén mobil hálózatok együttműködési problémái, - A mobil Internet Protokoll alkalmazásával kapcsolatos vizsgálatok, - Többfelhasználós detekciós módszerek a kódosztásos többszörös hozzáféréses mobil rendszerekben, - A heterogén mobil hálózatok forgalmi modellezése, - A mobil informatikai és távközlési hálózatok, rendszerek és szolgáltatások - biztonsági kérdései, - Kvantum számítástechnika és mérnöki alkalmazásai, - Útkeresési és csatornakijelölési algoritmusok fejlesztése és vizsgálata mobil hálózatok számára, alkalmazott gráfelmélet. A kutatásban résztvevők az eredményeket három megvédett PhD disszertációban, egy benyújtás előtt álló akadémiai doktori értekezésben és több beadás előtt álló PhD értekezésben használták fel. A tudományos iskola publikációs listája 135 elemből áll. | The members of the Scientific School have got new results in the following scientific fields: - Mobile IP, all IP networks, - Routing algorithms, - Hand-over algorithms, - Interworking of heterogeneous mobile technologies, - Quality of services (QoS), - Security problems of mobile and information networks and systems, - Multi-user detection, - Code division multiple access, - Traffic modeling, - Code construction for code division technologies, - Quantum computing, - Graph theory, - Combinatorial optimization. On the above mentioned scientific field we have the most important results in the following areas: - Interoperability issues of heterogeneous mobile networks, - Investigations on the applicability of mobile Internet Protocol, - Multi-user detection methods in code division multiple access systems, - Traffic models of heterogeneous mobile networks, - Security issues of mobile information and telecommunication networks, systems and services, - Quantum computing and its engineering applications, - Development and research of routing and channel assigning algorithms for mobile networks, application of the graph theory. The participants of the research used their results in three defended PhD theses, in a dissertation for DSc title, and in some other PhD theses before the final process. The number of the publications of the Scientific School is 135