8,290 research outputs found
Topology Discovery of Sparse Random Graphs With Few Participants
We consider the task of topology discovery of sparse random graphs using
end-to-end random measurements (e.g., delay) between a subset of nodes,
referred to as the participants. The rest of the nodes are hidden, and do not
provide any information for topology discovery. We consider topology discovery
under two routing models: (a) the participants exchange messages along the
shortest paths and obtain end-to-end measurements, and (b) additionally, the
participants exchange messages along the second shortest path. For scenario
(a), our proposed algorithm results in a sub-linear edit-distance guarantee
using a sub-linear number of uniformly selected participants. For scenario (b),
we obtain a much stronger result, and show that we can achieve consistent
reconstruction when a sub-linear number of uniformly selected nodes
participate. This implies that accurate discovery of sparse random graphs is
tractable using an extremely small number of participants. We finally obtain a
lower bound on the number of participants required by any algorithm to
reconstruct the original random graph up to a given edit distance. We also
demonstrate that while consistent discovery is tractable for sparse random
graphs using a small number of participants, in general, there are graphs which
cannot be discovered by any algorithm even with a significant number of
participants, and with the availability of end-to-end information along all the
paths between the participants.Comment: A shorter version appears in ACM SIGMETRICS 2011. This version is
scheduled to appear in J. on Random Structures and Algorithm
TopCom: Index for Shortest Distance Query in Directed Graph
Finding shortest distance between two vertices in a graph is an important
problem due to its numerous applications in diverse domains, including
geo-spatial databases, social network analysis, and information retrieval.
Classical algorithms (such as, Dijkstra) solve this problem in polynomial time,
but these algorithms cannot provide real-time response for a large number of
bursty queries on a large graph. So, indexing based solutions that pre-process
the graph for efficiently answering (exactly or approximately) a large number
of distance queries in real-time is becoming increasingly popular. Existing
solutions have varying performance in terms of index size, index building time,
query time, and accuracy. In this work, we propose T OP C OM , a novel
indexing-based solution for exactly answering distance queries. Our experiments
with two of the existing state-of-the-art methods (IS-Label and TreeMap) show
the superiority of T OP C OM over these two methods considering scalability and
query time. Besides, indexing of T OP C OM exploits the DAG (directed acyclic
graph) structure in the graph, which makes it significantly faster than the
existing methods if the SCCs (strongly connected component) of the input graph
are relatively small
The covert set-cover problem with application to Network Discovery
We address a version of the set-cover problem where we do not know the sets
initially (and hence referred to as covert) but we can query an element to find
out which sets contain this element as well as query a set to know the
elements. We want to find a small set-cover using a minimal number of such
queries. We present a Monte Carlo randomized algorithm that approximates an
optimal set-cover of size within factor with high probability
using queries where is the input size.
We apply this technique to the network discovery problem that involves
certifying all the edges and non-edges of an unknown -vertices graph based
on layered-graph queries from a minimal number of vertices. By reducing it to
the covert set-cover problem we present an -competitive Monte
Carlo randomized algorithm for the covert version of network discovery problem.
The previously best known algorithm has a competitive ratio of and therefore our result achieves an exponential improvement
Small-world networks, distributed hash tables and the e-resource discovery problem
Resource discovery is one of the most important underpinning problems behind producing a scalable,
robust and efficient global infrastructure for e-Science. A number of approaches to the resource discovery
and management problem have been made in various computational grid environments and prototypes
over the last decade. Computational resources and services in modern grid and cloud environments can be
modelled as an overlay network superposed on the physical network structure of the Internet and World
Wide Web. We discuss some of the main approaches to resource discovery in the context of the general
properties of such an overlay network. We present some performance data and predicted properties based
on algorithmic approaches such as distributed hash table resource discovery and management. We describe
a prototype system and use its model to explore some of the known key graph aspects of the global
resource overlay network - including small-world and scale-free properties
An introduction to Graph Data Management
A graph database is a database where the data structures for the schema
and/or instances are modeled as a (labeled)(directed) graph or generalizations
of it, and where querying is expressed by graph-oriented operations and type
constructors. In this article we present the basic notions of graph databases,
give an historical overview of its main development, and study the main current
systems that implement them
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