24,196 research outputs found
Content Distribution by Multiple Multicast Trees and Intersession Cooperation: Optimal Algorithms and Approximations
In traditional massive content distribution with multiple sessions, the
sessions form separate overlay networks and operate independently, where some
sessions may suffer from insufficient resources even though other sessions have
excessive resources. To cope with this problem, we consider the universal
swarming approach, which allows multiple sessions to cooperate with each other.
We formulate the problem of finding the optimal resource allocation to maximize
the sum of the session utilities and present a subgradient algorithm which
converges to the optimal solution in the time-average sense. The solution
involves an NP-hard subproblem of finding a minimum-cost Steiner tree. We cope
with this difficulty by using a column generation method, which reduces the
number of Steiner-tree computations. Furthermore, we allow the use of
approximate solutions to the Steiner-tree subproblem. We show that the
approximation ratio to the overall problem turns out to be no less than the
reciprocal of the approximation ratio to the Steiner-tree subproblem.
Simulation results demonstrate that universal swarming improves the performance
of resource-poor sessions with negligible impact to resource-rich sessions. The
proposed approach and algorithm are expected to be useful for
infrastructure-based content distribution networks with long-lasting sessions
and relatively stable network environment
Robust and MaxMin Optimization under Matroid and Knapsack Uncertainty Sets
Consider the following problem: given a set system (U,I) and an edge-weighted
graph G = (U, E) on the same universe U, find the set A in I such that the
Steiner tree cost with terminals A is as large as possible: "which set in I is
the most difficult to connect up?" This is an example of a max-min problem:
find the set A in I such that the value of some minimization (covering) problem
is as large as possible.
In this paper, we show that for certain covering problems which admit good
deterministic online algorithms, we can give good algorithms for max-min
optimization when the set system I is given by a p-system or q-knapsacks or
both. This result is similar to results for constrained maximization of
submodular functions. Although many natural covering problems are not even
approximately submodular, we show that one can use properties of the online
algorithm as a surrogate for submodularity.
Moreover, we give stronger connections between max-min optimization and
two-stage robust optimization, and hence give improved algorithms for robust
versions of various covering problems, for cases where the uncertainty sets are
given by p-systems and q-knapsacks.Comment: 17 pages. Preliminary version combining this paper and
http://arxiv.org/abs/0912.1045 appeared in ICALP 201
Perfect Omniscience, Perfect Secrecy and Steiner Tree Packing
We consider perfect secret key generation for a ``pairwise independent
network'' model in which every pair of terminals share a random binary string,
with the strings shared by distinct terminal pairs being mutually independent.
The terminals are then allowed to communicate interactively over a public
noiseless channel of unlimited capacity. All the terminals as well as an
eavesdropper observe this communication. The objective is to generate a perfect
secret key shared by a given set of terminals at the largest rate possible, and
concealed from the eavesdropper.
First, we show how the notion of perfect omniscience plays a central role in
characterizing perfect secret key capacity. Second, a multigraph representation
of the underlying secrecy model leads us to an efficient algorithm for perfect
secret key generation based on maximal Steiner tree packing. This algorithm
attains capacity when all the terminals seek to share a key, and, in general,
attains at least half the capacity. Third, when a single ``helper'' terminal
assists the remaining ``user'' terminals in generating a perfect secret key, we
give necessary and sufficient conditions for the optimality of the algorithm;
also, a ``weak'' helper is shown to be sufficient for optimality.Comment: accepted to the IEEE Transactions on Information Theor
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