35,566 research outputs found
On Compact Routing for the Internet
While there exist compact routing schemes designed for grids, trees, and
Internet-like topologies that offer routing tables of sizes that scale
logarithmically with the network size, we demonstrate in this paper that in
view of recent results in compact routing research, such logarithmic scaling on
Internet-like topologies is fundamentally impossible in the presence of
topology dynamics or topology-independent (flat) addressing. We use analytic
arguments to show that the number of routing control messages per topology
change cannot scale better than linearly on Internet-like topologies. We also
employ simulations to confirm that logarithmic routing table size scaling gets
broken by topology-independent addressing, a cornerstone of popular
locator-identifier split proposals aiming at improving routing scaling in the
presence of network topology dynamics or host mobility. These pessimistic
findings lead us to the conclusion that a fundamental re-examination of
assumptions behind routing models and abstractions is needed in order to find a
routing architecture that would be able to scale ``indefinitely.''Comment: This is a significantly revised, journal version of cs/050802
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
On fast planning of suboptimal paths amidst polygonal obstacles in plane
AbstractThe problem of planning a path for a point robot from a source point s to a destination point d so as to avoid a set of polygonal obstacles in plane is considered. Using well-known methods, a shortest path from s to d can be computed with a time complexity of O(n2) where n is the total number of obstacle vertices. The focus here is in 1.(a) planning paths faster at the expense of setting for suboptimal path lengths and2.(b) performance analysis of simple and/or well-known suboptimal methods.
A method that enables a hierarchical implementation of any path planning algorithm with no increase in the worst-case time complexity, is presented; this implementation enables fast planning of simple paths. Then methods are presented based on the Voronoi diagrams, trapezoidal decomposition and triangulation, which compute (suboptimal) paths in O(n√log n) time with the preprocessing costs of O(n log n), O(n2) and O(n log n), respectively. Using existing navigational algorithms for unknown terrains, algorithms that run in O(n log n) time (after preprocessing) and yield suboptimal paths, are presented. For all these algorithms, upper bounds on the path lengths are estimated in terms of the shortest of the obstacles, etc
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Extending TRANSIMS Technology to an Integrated Multilevel Representation
The TRANSIMS system developed at Los Alamos in the USA over the past decade is a world leader in providing an integrated land-use transportation dynamical model for large areas with a million or more inhabitants. TRANSIMS uses standard survey data to create synthetic micropopulations, including family structure, to simulate trip making and emergent traffic dynamics. We propose to extend TRANSIMS by adapting it to a new multi-level representation, allowing dynamics to be algebraically integrated at the micro-, meso- and macro-levels. The new representation builds a lattice hierarchy in a way that integrates non-partitional hierarchies of links and routes based on the usual hierarchy of geographical zones, e.g. neighbourhoods, districts, cities, counties and countries. Applying the representation to a big city starts by defining sets of zones at different levels. At the first level, N, is the street. This can be subdivided to building plots at level N-1, buildings at level N-2, and even rooms at level N-3. At level N+1 are the neighbourhoods, at level N+2 is the set of district zones (each of them containing the different neighbourhoods in the previous level), and at the top level N+3 (in this case), is just one zone, the city itself. If a larger study area is to be considered, we would have a whole set of N+3 zones defining N+4-level areas, and so on, extending to the level of counties, countries or even continents. This paper will explain the fundamentals of TRANSIMS technology and compare it to other systems. We will show how TRANSIMS and the new multi-level representation can be brought together to give new insights into the macro-dynamics of very large road systems such as London, England and even the whole of Europe
Hierarchical Time-Dependent Oracles
We study networks obeying \emph{time-dependent} min-cost path metrics, and
present novel oracles for them which \emph{provably} achieve two unique
features: % (i) \emph{subquadratic} preprocessing time and space,
\emph{independent} of the metric's amount of disconcavity; % (ii)
\emph{sublinear} query time, in either the network size or the actual
Dijkstra-Rank of the query at hand
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