Overcoming the inherent challenges.

Given a set of data graphs and a query graph, graph isomorphism query processing is the problem of finding all the data graphs that are isomorphic to the query graph. Graph isomorphism query processing is a core problem in graph analysis of various application domains. In existing approaches, index construction or query processing takes much time as the graph sizes increase. In this paper, we propose an efficient algorithm for graph isomorphism query processing. We introduce the color-label distribution which represents the canonical coloring of a vertex-labeled graph. Based on degree sequences and color-label distributions, we introduce a two-level index, which helps us efficiently solve graph isomorphism query processing. Experimental results on real datasets show that the proposed algorithm is orders of magnitude faster than the state-of-the-art algorithms in terms of index construction time, and it runs faster than existing algorithms in terms of query processing time as the graph sizes increase.

Graph isomorphism is a core problem in graph analysis of various application domains. Given two graphs, the graph isomorphism problem is to determine whether there exists an isomorphism between them. As real-world graphs are getting bigger and bigger, applications demand practically fast algorithms that can run on large-scale graphs. However, existing approaches such as graph canonization and subgraph isomorphism show limited performances on large-scale graphs either in time or space. In this paper, we propose a new approach to graph isomorphism, which is the framework of pairwise color refinement and efficient backtracking. The main features of our approach are: (1) pairwise color refinement and binary cell mapping (2) compressed CS (candidate space), and (3) partial failing set, which together lead to a much faster and scalable algorithm for graph isomorphism. Extensive experiments with real-world datasets show that our approach outperforms state-of-the-art algorithms by up to orders of magnitude in terms of running time.

AbstractLessons learned from the first five years of Georgia Tech's Online Master of Science in Computer Science program.

This paper reviews the first 40 years in the life of suffix trees, their many incarnations, and their applications. The paper is non-technical but assumes some familiarity with the structures and constructions discussed. It is not meant to be exhaustive. It is meant to be a tribute to a ubiquitous tool of string matching — the suffix tree and its variants — and one of the most persistent subjects of study in the theory of algorithms.

Tracing the first four decades in the life of suffix trees, their many incarnations, and their applications.

This paper presents a real-time randomized streaming string matching algorithm that uses O(logm) space. The algorithm only makes one-sided small probability false-positive errors, possibly reporting phantom occurrences of the pattern, but never misses an actual occurrence.

This chapter provides comprehensive analysis of several generations of mobility protocols (e.g., 1G, 2G, 3G, and 4G) in order to extrapolate the common abstract functions during a mobility event. It describes how discovery, configuration, authentication, security association, and media routing functions associated with a mobile's handoff are performed for each of the cellular and IP-based mobility protocols and then maps the respective network parameters for these mobility protocols to each of the common mobility functions. A comparative analysis and extrapolation of the abstract primitives can help to design an optimized mobility system with a given resource constraints and build the optimization mechanisms for each these mobility functions.

This chapter highlights the key mobility optimization techniques that are developed to optimize several basic operations of a mobility event in various layers, namely layer 2, layer 3 and application layer and describes the associated key principles these optimization techniques are based on. In particular, this chapter describes the key optimization techniques associated with some of the fundamental mobility functions, namely discovery, authentication, configuration, security association, binding update, media rerouting, route optimization and cross layer triggers. These optimization techniques are based on a few fundamental principles, such as reduction of the number of signaling messages during the basic operations, minimizing the traversal distance of the data, reduction of data and signaling overhead, minimization of lookup cost, caching, parallelization of sequential handoff operations, proactive operations, cross-layer triggers, and localization of binding updates. This chapter also demonstrates application of these optimization techniques for various handoff components by way of experimental results using the testbed that the authors have built.

Free Access RDF Schema for Application Layer Discovery Ashutosh Dutta, Ashutosh Dutta AT&T, USASearch for more papers by this authorHenning Schulzrinne, Henning Schulzrinne Columbia University, USASearch for more papers by this author Book Author(s):Ashutosh Dutta, Ashutosh Dutta AT&T, USASearch for more papers by this authorHenning Schulzrinne, Henning Schulzrinne Columbia University, USASearch for more papers by this author First published: 28 March 2014 https://doi.org/10.1002/9781119945505.app1 AboutPDFPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShareShare a linkShare onFacebookTwitterLinked InRedditWechat Mobility Protocols and Handover Optimization: Design, Evaluation and Application RelatedInformation

This paper reviews the first 40 years in the life of textual inverted indexes, their many incarnations, and their applications. The paper is non-technical and assumes some familiarity with the structures and constructions discussed. It is not meant to be exhaustive. It is meant to be a tribute to a ubiquitous tool of string matching - the suffix tree and its variants - and one of the most persistent subjects of study in the theory of algorithms.

Twenty five years ago in a paper titled “Open Problems in Stringology” I listed thirteen open problems in a field I called Stringology. The first part of the talk will revisit the list. Some problems were solved, others were partially solved and some resisted any progress. The second part of the talk will review some recent results in Stringology, namely algorithms in the streaming model. In this model, the algorithms cannot store the entire input string(s) and can use only very limited space. Surprisingly, efficient algorithms were discovered for a number of string problems. The talk will conclude with new open problems that are raised by these new results.

wards a theory of nearly constant time parallel algorithms. In FOCS '91, pages 698{710, Octo-ber 1991. 11] Michael T. Goodrich. Using approximation algorithms to design parallel algorithms that may ignore processor allocation. 18] Yossi Matias and Uzi Vishkin. Converting high probability into nearly-constant time|with applications to parallel hashing. In STOC '91, pages 307{316, 1991. 19] Sanguthevar Rajasekaran and John H. Reif. Optimal and sublogarithmic time randomized parallel sorting algorithms. integer coordinates, one can produce a triangulation of S in O(T PIS (n) + lglg n) time, with high probability, using an optimal number of processors on a random-ized CRCW PRAM. We have shown above that we can solve problems deened on point sets with integer coordinates very fast in parallel. In the subsections that follow we show analogous results for lines. 4.3 2-Dimensional Hidden Line Elimination Suppose we are given a set S of n planar line segments that do not intersect, except possibly at endpoints. Suppose further that the endpoints of the segments in S have integer coordinates. The 2-dimensional hidden line elimination problem is to produce a sorted list of pairs (x i ; y i) such that x i is the x-coordinate of a segment endpoint and y i is the y-coordinate of the point visible from (0; ?1) at x i (i.e., the lowest point on a segment in S that intersects the line x = x i). Intuitively , one imagines the point (0; ?1) to be the \eye" location, and the problem is to produce a representation of what that eye can see assuming each segment is opaque. We show below how to solve this problem in O(T PIS (n)) time using O(n lg n) work. The work complexity matches that of the fastest deterministic algorithm , which is due to Atallah, Cole, and Goodrich 3]; their algorithm takes O(lg n) time, however. 1. Sort the endpoints of S by x-coordinates by a call to padded sort. 2. Build a binary tree T \on top" of these x-coordinates. Each leaf v of T is associated with a vertical slab (v), which is the set of all points whose x-coordinates fall in the x-interval associated with this leaf. Deene for each internal node v a slab (v) that is the union of the x-coordinate intervals deened by v's descendants. (This can all be easily implemented in O(1) time.) 3. For any segment s = pq, …

We describe an algorithm that constructs for a given set of (functional and multivalued) dependencies Σ and a set of attributes X, the dependency basis of X. The algorithm runs in time O(min(k,log p)|Σ|), where p is the number of sets in the dependency basis of X and k is the number of dependencies in Σ. A variant of the algorithm tests whether a dependency σ is implied by Σ in time O(min(k,log p) |Σ|), where p is the number of sets in the dependency basis of the left-hand side of σ that intersect the right-hand side of σ. Whenever all the dependencies in ΣU{σ} are functional dependencies these algorithms are linear time.

We present the notion of "Dynamic Re-sharing Verifiable Secret Sharing" (VSS) where the dealing of shares is dynamically and randomly refreshed (without changing or corrupting the secret). It works against the threat of the recently considered mobile adversary that may control all the trustees, but only a bounded number thereof at any time period. VSS enables a dealer to distribute its secret to a set of trustees, so that they are assured that the sharing is valid and that they can open it later, and further no small group of trustees can open it prematurely. Recently, such sharing of cryptographic tools gained much attention, e.g., in the context of "key escrow cryptography" where a user enables a group of trustees to potentially open its information (when authorized by the court). Our dynamic-sharing VSS allows for mobile adversary attacking different sets of trustees at different time periods (modeling, e.g., network viruses that get spread as well as get eliminated). Technically, we concentrate on simple direct methods that are combinatorial and number-theoretic in nature, and employ only simple public-key functions. (All previous schemes withstanding linear number of faults embedded secrets in polynomials which we do not do). In addition, our protocols are constant round. The work is a sequence of reductions. We reduce t(t

Given a text string, a pattern string, and an integer k, a new algorithm for finding all occurrences of the pattern string in the text string with at most k differences is presented. Both its theoretical and practical variants improve the known algorithms.

We have described a number of algorithmic tools that have been found useful in the construction of parallel algorithms; among these are prefix computation, ranking, Euler tours, ear decomposition, and matrix calculations. We have also described some of the applications of these tools, and listed many other applications. These algorithms seem likely to be useful not only in their own right, but also as examples of ways to break up other problems into parts suitable for parallel solution.