27,234 research outputs found
Optimizing IGP Link Costs for Improving IP-level Resilience
Recently, major vendors have introduced new router
platforms to the market that support fast IP-level failure pro-
tection out of the box. The implementations are based on the
IP Fast ReRoute–Loop Free Alternates (LFA) standard. LFA
is simple, unobtrusive, and easily deployable. This simplicity,
however, comes at a severe price, in that LFA usually cannot
protect all possible failure scenarios. In this paper, we give new
graph theoretical tools for analyzing LFA failure case coverage
and we seek ways for improvement. In particular, we investigate
how to optimize IGP link costs to maximize the number of
protected failure scenarios, we show that this problem is NP-
complete even in a very restricted formulation, and we give exact
and approximate algorithms to solve it. Our simulation studies
show that a deliberate selection of IGP costs can bring many
networks close to complete LFA-based protection
Lower Bounds in the Preprocessing and Query Phases of Routing Algorithms
In the last decade, there has been a substantial amount of research in
finding routing algorithms designed specifically to run on real-world graphs.
In 2010, Abraham et al. showed upper bounds on the query time in terms of a
graph's highway dimension and diameter for the current fastest routing
algorithms, including contraction hierarchies, transit node routing, and hub
labeling. In this paper, we show corresponding lower bounds for the same three
algorithms. We also show how to improve a result by Milosavljevic which lower
bounds the number of shortcuts added in the preprocessing stage for contraction
hierarchies. We relax the assumption of an optimal contraction order (which is
NP-hard to compute), allowing the result to be applicable to real-world
instances. Finally, we give a proof that optimal preprocessing for hub labeling
is NP-hard. Hardness of optimal preprocessing is known for most routing
algorithms, and was suspected to be true for hub labeling
Route Planning in Transportation Networks
We survey recent advances in algorithms for route planning in transportation
networks. For road networks, we show that one can compute driving directions in
milliseconds or less even at continental scale. A variety of techniques provide
different trade-offs between preprocessing effort, space requirements, and
query time. Some algorithms can answer queries in a fraction of a microsecond,
while others can deal efficiently with real-time traffic. Journey planning on
public transportation systems, although conceptually similar, is a
significantly harder problem due to its inherent time-dependent and
multicriteria nature. Although exact algorithms are fast enough for interactive
queries on metropolitan transit systems, dealing with continent-sized instances
requires simplifications or heavy preprocessing. The multimodal route planning
problem, which seeks journeys combining schedule-based transportation (buses,
trains) with unrestricted modes (walking, driving), is even harder, relying on
approximate solutions even for metropolitan inputs.Comment: This is an updated version of the technical report MSR-TR-2014-4,
previously published by Microsoft Research. This work was mostly done while
the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at
Microsoft Research Silicon Valle
Fast Routing Table Construction Using Small Messages
We describe a distributed randomized algorithm computing approximate
distances and routes that approximate shortest paths. Let n denote the number
of nodes in the graph, and let HD denote the hop diameter of the graph, i.e.,
the diameter of the graph when all edges are considered to have unit weight.
Given 0 < eps <= 1/2, our algorithm runs in weak-O(n^(1/2 + eps) + HD)
communication rounds using messages of O(log n) bits and guarantees a stretch
of O(eps^(-1) log eps^(-1)) with high probability. This is the first
distributed algorithm approximating weighted shortest paths that uses small
messages and runs in weak-o(n) time (in graphs where HD in weak-o(n)). The time
complexity nearly matches the lower bounds of weak-Omega(sqrt(n) + HD) in the
small-messages model that hold for stateless routing (where routing decisions
do not depend on the traversed path) as well as approximation of the weigthed
diameter. Our scheme replaces the original identifiers of the nodes by labels
of size O(log eps^(-1) log n). We show that no algorithm that keeps the
original identifiers and runs for weak-o(n) rounds can achieve a
polylogarithmic approximation ratio.
Variations of our techniques yield a number of fast distributed approximation
algorithms solving related problems using small messages. Specifically, we
present algorithms that run in weak-O(n^(1/2 + eps) + HD) rounds for a given 0
< eps <= 1/2, and solve, with high probability, the following problems:
- O(eps^(-1))-approximation for the Generalized Steiner Forest (the running
time in this case has an additive weak-O(t^(1 + 2eps)) term, where t is the
number of terminals);
- O(eps^(-2))-approximation of weighted distances, using node labels of size
O(eps^(-1) log n) and weak-O(n^(eps)) bits of memory per node;
- O(eps^(-1))-approximation of the weighted diameter;
- O(eps^(-3))-approximate shortest paths using the labels 1,...,n.Comment: 40 pages, 2 figures, extended abstract submitted to STOC'1
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