10,257 research outputs found
Optimum Multi-Dimensional Interval Routing Schemes on Networks with Dynamic Cost Links
One of the fundamental tasks in any distributed computing system is routing messages between pairs of nodes. An Interval Routing Scheme (IRS) is a~space efficient way of routing messages in a network. The problem of characterizing graphs that support an IRS is a well-known problem and has been studied for some variants of IRS. It is natural to assume that the costs of links may vary over time (dynamic cost links) and to try to find an IRS which routes all messages on shortest paths (optimum IRS). In this paper, we study this problem for a~variant of IRS in which the labels assigned to the vertices are -ary integer tuples (-dimensional IRS). The only known results in this case are for specific graphs like hypercubes, -dimensional grids, or for the 1-dimensional case. We give a complete characterization for the class of networks supporting multi-dimensional strict and linear (no cyclic intervals) interval routing schemes with dynamic cost links
Matroids are Immune to Braess Paradox
The famous Braess paradox describes the following phenomenon: It might happen
that the improvement of resources, like building a new street within a
congested network, may in fact lead to larger costs for the players in an
equilibrium. In this paper we consider general nonatomic congestion games and
give a characterization of the maximal combinatorial property of strategy
spaces for which Braess paradox does not occur. In a nutshell, bases of
matroids are exactly this maximal structure. We prove our characterization by
two novel sensitivity results for convex separable optimization problems over
polymatroid base polyhedra which may be of independent interest.Comment: 21 page
Interval Routing Schemes for Circular-Arc Graphs
Interval routing is a space efficient method to realize a distributed routing
function. In this paper we show that every circular-arc graph allows a shortest
path strict 2-interval routing scheme, i.e., by introducing a global order on
the vertices and assigning at most two (strict) intervals in this order to the
ends of every edge allows to depict a routing function that implies exclusively
shortest paths. Since circular-arc graphs do not allow shortest path 1-interval
routing schemes in general, the result implies that the class of circular-arc
graphs has strict compactness 2, which was a hitherto open question.
Additionally, we show that the constructed 2-interval routing scheme is a
1-interval routing scheme with at most one additional interval assigned at each
vertex and we an outline algorithm to calculate the routing scheme for
circular-arc graphs in O(n^2) time, where n is the number of vertices.Comment: 17 pages, to appear in "International Journal of Foundations of
Computer Science
The complexity of the characterization of networks supporting shortest-path interval routing
AbstractInterval Routing is a routing method that was proposed in order to reduce the size of the routing tables by using intervals and was extensively studied and implemented. Some variants of the original method were also defined and studied. The question of characterizing networks which support optimal (i.e., shortest path) Interval Routing has been thoroughly investigated for each of the variants and under different models, with only partial answers, both positive and negative, given so far. In this paper, we study the characterization problem under the most basic model (the one unit cost), and with the most restrictive memory requirements (one interval per edge). We prove that this problem is NP-hard (even for the restricted class of graphs of diameter at most 3). Our result holds for all variants of Interval Routing. It significantly extends some related NP-hardness result, and implies that, unless P=NP, partial characterization results of some classes of networks which support shortest path Interval Routing, cannot be pushed further to lead to efficient characterizations for these classes
Towards a System Theoretic Approach to Wireless Network Capacity in Finite Time and Space
In asymptotic regimes, both in time and space (network size), the derivation
of network capacity results is grossly simplified by brushing aside queueing
behavior in non-Jackson networks. This simplifying double-limit model, however,
lends itself to conservative numerical results in finite regimes. To properly
account for queueing behavior beyond a simple calculus based on average rates,
we advocate a system theoretic methodology for the capacity problem in finite
time and space regimes. This methodology also accounts for spatial correlations
arising in networks with CSMA/CA scheduling and it delivers rigorous
closed-form capacity results in terms of probability distributions. Unlike
numerous existing asymptotic results, subject to anecdotal practical concerns,
our transient one can be used in practical settings: for example, to compute
the time scales at which multi-hop routing is more advantageous than single-hop
routing
Network Information Flow in Small World Networks
Recent results from statistical physics show that large classes of complex
networks, both man-made and of natural origin, are characterized by high
clustering properties yet strikingly short path lengths between pairs of nodes.
This class of networks are said to have a small-world topology. In the context
of communication networks, navigable small-world topologies, i.e. those which
admit efficient distributed routing algorithms, are deemed particularly
effective, for example in resource discovery tasks and peer-to-peer
applications. Breaking with the traditional approach to small-world topologies
that privileges graph parameters pertaining to connectivity, and intrigued by
the fundamental limits of communication in networks that exploit this type of
topology, we investigate the capacity of these networks from the perspective of
network information flow. Our contribution includes upper and lower bounds for
the capacity of standard and navigable small-world models, and the somewhat
surprising result that, with high probability, random rewiring does not alter
the capacity of a small-world network.Comment: 23 pages, 8 fitures, submitted to the IEEE Transactions on
Information Theory, November 200
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