3,792 research outputs found
Finding multiple maximally redundant trees in linear time
Redundant trees are directed spanning trees, which provide disjoint paths towards their roots. Therefore, this concept is widely applied in the literature both for providing protection and load sharing. The fastest algorithm can find multiple redundant trees, a pair of them rooted at each vertex, in linear time.
Unfortunately, edge- or vertex-redundant trees can only be found in 2-edge- or 2-vertex-connected graphs respectively. Therefore, the concept of maximally redundant trees was introduced, which can overcome this problem, and provides maximally disjoint paths towards the common root. In this paper, we propose the first linear time algorithm, which can compute a pair of maximally redundant trees rooted at not only one, but at each vertex
Efficient Batch Query Answering Under Differential Privacy
Differential privacy is a rigorous privacy condition achieved by randomizing
query answers. This paper develops efficient algorithms for answering multiple
queries under differential privacy with low error. We pursue this goal by
advancing a recent approach called the matrix mechanism, which generalizes
standard differentially private mechanisms. This new mechanism works by first
answering a different set of queries (a strategy) and then inferring the
answers to the desired workload of queries. Although a few strategies are known
to work well on specific workloads, finding the strategy which minimizes error
on an arbitrary workload is intractable. We prove a new lower bound on the
optimal error of this mechanism, and we propose an efficient algorithm that
approaches this bound for a wide range of workloads.Comment: 6 figues, 22 page
Throughput-Optimal Broadcast on Directed Acyclic Graphs
We study the problem of broadcasting packets in wireless networks. At each
time slot, a network controller activates non-interfering links and forwards
packets to all nodes at a common rate; the maximum rate is referred to as the
broadcast capacity of the wireless network. Existing policies achieve the
broadcast capacity by balancing traffic over a set of spanning trees, which are
difficult to maintain in a large and time-varying wireless network. We propose
a new dynamic algorithm that achieves the broadcast capacity when the
underlying network topology is a directed acyclic graph (DAG). This algorithm
utilizes local queue-length information, does not use any global topological
structures such as spanning trees, and uses the idea of in-order packet
delivery to all network nodes. Although the in-order packet delivery constraint
leads to degraded throughput in cyclic graphs, we show that it is throughput
optimal in DAGs and can be exploited to simplify the design and analysis of
optimal algorithms. Our simulation results show that the proposed algorithm has
superior delay performance as compared to tree-based approaches.Comment: To appear in the proceedings of INFOCOM, 201
Throughput-Optimal Multihop Broadcast on Directed Acyclic Wireless Networks
We study the problem of efficiently broadcasting packets in multi-hop
wireless networks. At each time slot the network controller activates a set of
non-interfering links and forwards selected copies of packets on each activated
link. A packet is considered jointly received only when all nodes in the
network have obtained a copy of it. The maximum rate of jointly received
packets is referred to as the broadcast capacity of the network. Existing
policies achieve the broadcast capacity by balancing traffic over a set of
spanning trees, which are difficult to maintain in a large and time-varying
wireless network. We propose a new dynamic algorithm that achieves the
broadcast capacity when the underlying network topology is a directed acyclic
graph (DAG). This algorithm is decentralized, utilizes local queue-length
information only and does not require the use of global topological structures
such as spanning trees. The principal technical challenge inherent in the
problem is the absence of work-conservation principle due to the duplication of
packets, which renders traditional queuing modelling inapplicable. We overcome
this difficulty by studying relative packet deficits and imposing in-order
delivery constraints to every node in the network. Although in-order packet
delivery, in general, leads to degraded throughput in graphs with cycles, we
show that it is throughput optimal in DAGs and can be exploited to simplify the
design and analysis of optimal algorithms. Our characterization leads to a
polynomial time algorithm for computing the broadcast capacity of any wireless
DAG under the primary interference constraints. Additionally, we propose an
extension of our algorithm which can be effectively used for broadcasting in
any network with arbitrary topology
Scalable and Efficient Multipath Routing: Complexity and Algorithms
A fundamental unsolved challenge in multipath
routing is to provide disjoint end-to-end paths, each one satisfying
certain operational goals (e.g., shortest possible), without overwhelming
the data plane with prohibitive amount of forwarding
state. In this paper, we study the problem of finding a pair
of shortest disjoint paths that can be represented by only two
forwarding table entries per destination. Building on prior work
on minimum length redundant trees, we show that the underlying
mathematical problem is NP-complete and we present heuristic
algorithms that improve the known complexity bounds from
cubic to the order of a single shortest path search. Finally, by
extensive simulations we find that it is possible to very closely
attain the absolute optimal path length with our algorithms (the
gap is just 1–5%), eventually opening the door for wide-scale
multipath routing deployments
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