28,141 research outputs found
Universal Loop-Free Super-Stabilization
We propose an univesal scheme to design loop-free and super-stabilizing
protocols for constructing spanning trees optimizing any tree metrics (not only
those that are isomorphic to a shortest path tree). Our scheme combines a novel
super-stabilizing loop-free BFS with an existing self-stabilizing spanning tree
that optimizes a given metric. The composition result preserves the best
properties of both worlds: super-stabilization, loop-freedom, and optimization
of the original metric without any stabilization time penalty. As case study we
apply our composition mechanism to two well known metric-dependent spanning
trees: the maximum-flow tree and the minimum degree spanning tree
An Axiomatic Approach to Routing
Information delivery in a network of agents is a key issue for large, complex
systems that need to do so in a predictable, efficient manner. The delivery of
information in such multi-agent systems is typically implemented through
routing protocols that determine how information flows through the network.
Different routing protocols exist each with its own benefits, but it is
generally unclear which properties can be successfully combined within a given
algorithm. We approach this problem from the axiomatic point of view, i.e., we
try to establish what are the properties we would seek to see in such a system,
and examine the different properties which uniquely define common routing
algorithms used today.
We examine several desirable properties, such as robustness, which ensures
adding nodes and edges does not change the routing in a radical, unpredictable
ways; and properties that depend on the operating environment, such as an
"economic model", where nodes choose their paths based on the cost they are
charged to pass information to the next node. We proceed to fully characterize
minimal spanning tree, shortest path, and weakest link routing algorithms,
showing a tight set of axioms for each.Comment: In Proceedings TARK 2015, arXiv:1606.0729
Distributed Approximation of Minimum Routing Cost Trees
We study the NP-hard problem of approximating a Minimum Routing Cost Spanning
Tree in the message passing model with limited bandwidth (CONGEST model). In
this problem one tries to find a spanning tree of a graph over nodes
that minimizes the sum of distances between all pairs of nodes. In the
considered model every node can transmit a different (but short) message to
each of its neighbors in each synchronous round. We provide a randomized
-approximation with runtime for
unweighted graphs. Here, is the diameter of . This improves over both,
the (expected) approximation factor and the runtime
of the best previously known algorithm.
Due to stating our results in a very general way, we also derive an (optimal)
runtime of when considering -approximations as done by the
best previously known algorithm. In addition we derive a deterministic
-approximation
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