8,205 research outputs found
Network Interdiction Using Adversarial Traffic Flows
Traditional network interdiction refers to the problem of an interdictor
trying to reduce the throughput of network users by removing network edges. In
this paper, we propose a new paradigm for network interdiction that models
scenarios, such as stealth DoS attack, where the interdiction is performed
through injecting adversarial traffic flows. Under this paradigm, we first
study the deterministic flow interdiction problem, where the interdictor has
perfect knowledge of the operation of network users. We show that the problem
is highly inapproximable on general networks and is NP-hard even when the
network is acyclic. We then propose an algorithm that achieves a logarithmic
approximation ratio and quasi-polynomial time complexity for acyclic networks
through harnessing the submodularity of the problem. Next, we investigate the
robust flow interdiction problem, which adopts the robust optimization
framework to capture the case where definitive knowledge of the operation of
network users is not available. We design an approximation framework that
integrates the aforementioned algorithm, yielding a quasi-polynomial time
procedure with poly-logarithmic approximation ratio for the more challenging
robust flow interdiction. Finally, we evaluate the performance of the proposed
algorithms through simulations, showing that they can be efficiently
implemented and yield near-optimal solutions
Lattice Point Asymptotics and Volume Growth on Teichmuller space
We apply some of the ideas of the Ph.D. Thesis of G. A. Margulis to
Teichmuller space. Let x be a point in Teichmuller space, and let B_R(x) be the
ball of radius R centered at x (with distances measured in the Teichmuller
metric).
We obtain asymptotic formulas as R tends to infinity for the volume of
B_R(x), and also for for the cardinality of the intersection of B_R(x) with an
orbit of the mapping class group.Comment: 45 Pages, 2 figures. Minor correction
A Maximum Principle for Combinatorial Yamabe Flow
This article studies a discrete geometric structure on triangulated manifolds
and an associated curvature flow (combinatorial Yamabe flow). The associated
evolution of curvature appears to be like a heat equation on graphs, but it can
be shown to not satisfy the maximum principle. The notion of a parabolic-like
operator is introduced as an operator which satisfies the maximum principle,
but may not be parabolic in the usual sense of operators on graphs. A maximum
principle is derived for the curvature of combinatorial Yamabe flow under
certain assumptions on the triangulation, and hence the heat operator is shown
to be parabolic-like. The maximum principle then allows a characterization of
the curvature as well was a proof of long term existence of the flow.Comment: 20 pages, this is an almost entirely different paper. Some elements
of the old version are in the paper arxiv:math.MG/050618
Flow Decomposition With Subpath Constraints
Flow network decomposition is a natural model for problems where we are given a flow network arising from superimposing a set of weighted paths and would like to recover the underlying data, i.e., decompose the flow into the original paths and their weights. Thus, variations on flow decomposition are often used as subroutines in multiassembly problems such as RNA transcript assembly. In practice, we frequently have access to information beyond flow values in the form of subpaths, and many tools incorporate these heuristically. But despite acknowledging their utility in practice, previous work has not formally addressed the effect of subpath constraints on the accuracy of flow network decomposition approaches. We formalize the flow decomposition with subpath constraints problem, give the first algorithms for it, and study its usefulness for recovering ground truth decompositions. For finding a minimum decomposition, we propose both a heuristic and an FPTalgorithm. Experiments on RNA transcript datasets show that for instances with larger solution path sets, the addition of subpath constraints finds 13% more ground truth solutions when minimal decompositions are found exactly, and 30% more ground truth solutions when minimal decompositions are found heuristically.Peer reviewe
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