9,869 research outputs found
Routing in Histograms
Let be an -monotone orthogonal polygon with vertices. We call
a simple histogram if its upper boundary is a single edge; and a double
histogram if it has a horizontal chord from the left boundary to the right
boundary. Two points and in are co-visible if and only if the
(axis-parallel) rectangle spanned by and completely lies in . In the
-visibility graph of , we connect two vertices of with an edge
if and only if they are co-visible.
We consider routing with preprocessing in . We may preprocess to
obtain a label and a routing table for each vertex of . Then, we must be
able to route a packet between any two vertices and of , where each
step may use only the label of the target node , the routing table and
neighborhood of the current node, and the packet header.
We present a routing scheme for double histograms that sends any data packet
along a path whose length is at most twice the (unweighted) shortest path
distance between the endpoints. In our scheme, the labels, routing tables, and
headers need bits. For the case of simple histograms, we obtain a
routing scheme with optimal routing paths, -bit labels, one-bit
routing tables, and no headers.Comment: 18 pages, 11 figure
Edge overload breakdown in evolving networks
We investigate growing networks based on Barabasi and Albert's algorithm for
generating scale-free networks, but with edges sensitive to overload breakdown.
the load is defined through edge betweenness centrality. We focus on the
situation where the average number of connections per vertex is, as the number
of vertices, linearly increasing in time. After an initial stage of growth, the
network undergoes avalanching breakdowns to a fragmented state from which it
never recovers. This breakdown is much less violent if the growth is by random
rather than preferential attachment (as defines the Barabasi and Albert model).
We briefly discuss the case where the average number of connections per vertex
is constant. In this case no breakdown avalanches occur. Implications to the
growth of real-world communication networks are discussed.Comment: To appear in Phys. Rev.
Statistical structures for internet-scale data management
Efficient query processing in traditional database management systems relies on statistics on base data. For centralized systems, there is a rich body of research results on such statistics, from simple aggregates to more elaborate synopses such as sketches and histograms. For Internet-scale distributed systems, on the other hand, statistics management still poses major challenges. With the work in this paper we aim to endow peer-to-peer data management over structured overlays with the power associated with such statistical information, with emphasis on meeting the scalability challenge. To this end, we first contribute efficient, accurate, and decentralized algorithms that can compute key aggregates such as Count, CountDistinct, Sum, and Average. We show how to construct several types of histograms, such as simple Equi-Width, Average-Shifted Equi-Width, and Equi-Depth histograms. We present a full-fledged open-source implementation of these tools for distributed statistical synopses, and report on a comprehensive experimental performance evaluation, evaluating our contributions in terms of efficiency, accuracy, and scalability
Using data network metrics, graphics, and topology to explore network characteristics
Yehuda Vardi introduced the term network tomography and was the first to
propose and study how statistical inverse methods could be adapted to attack
important network problems (Vardi, 1996). More recently, in one of his final
papers, Vardi proposed notions of metrics on networks to define and measure
distances between a network's links, its paths, and also between different
networks (Vardi, 2004). In this paper, we apply Vardi's general approach for
network metrics to a real data network by using data obtained from special data
network tools and testing procedures presented here. We illustrate how the
metrics help explicate interesting features of the traffic characteristics on
the network. We also adapt the metrics in order to condition on traffic passing
through a portion of the network, such as a router or pair of routers, and show
further how this approach helps to discover and explain interesting network
characteristics.Comment: Published at http://dx.doi.org/10.1214/074921707000000058 in the IMS
Lecture Notes Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
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