1,244 research outputs found
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
Triangles and Girth in Disk Graphs and Transmission Graphs
Let S subset R^2 be a set of n sites, where each s in S has an associated radius r_s > 0. The disk graph D(S) is the undirected graph with vertex set S and an undirected edge between two sites s, t in S if and only if |st| <= r_s + r_t, i.e., if the disks with centers s and t and respective radii r_s and r_t intersect. Disk graphs are used to model sensor networks. Similarly, the transmission graph T(S) is the directed graph with vertex set S and a directed edge from a site s to a site t if and only if |st| <= r_s, i.e., if t lies in the disk with center s and radius r_s.
We provide algorithms for detecting (directed) triangles and, more generally, computing the length of a shortest cycle (the girth) in D(S) and in T(S). These problems are notoriously hard in general, but better solutions exist for special graph classes such as planar graphs. We obtain similarly efficient results for disk graphs and for transmission graphs. More precisely, we show that a shortest (Euclidean) triangle in D(S) and in T(S) can be found in O(n log n) expected time, and that the (weighted) girth of D(S) can be found in O(n log n) expected time. For this, we develop new tools for batched range searching that may be of independent interest
An Improved Algorithm for Incremental DFS Tree in Undirected Graphs
Depth first search (DFS) tree is one of the most well-known data structures
for designing efficient graph algorithms. Given an undirected graph
with vertices and edges, the textbook algorithm takes time to
construct a DFS tree. In this paper, we study the problem of maintaining a DFS
tree when the graph is undergoing incremental updates. Formally, we show: Given
an arbitrary online sequence of edge or vertex insertions, there is an
algorithm that reports a DFS tree in worst case time per operation, and
requires preprocessing time.
Our result improves the previous worst case update time
algorithm by Baswana et al. and the time by Nakamura and
Sadakane, and matches the trivial lower bound when it is required
to explicitly output a DFS tree.
Our result builds on the framework introduced in the breakthrough work by
Baswana et al., together with a novel use of a tree-partition lemma by Duan and
Zhan, and the celebrated fractional cascading technique by Chazelle and Guibas
Social Influences in Recommendation Systems
Social networking sites such as Flickr and Facebook allow users to share
content with family, friends, and interest groups. Also, tags can often assign
to resources. In the previous research using few association rules FAR, we have
seen that high-quality and efficient association-based tag recommendation is
possible, but the set-up that we considered was very generic and did not take
social information into account. The proposed method in the previous paper,
FAR, in particular, exhibited a favorable trade-off between recommendation
quality and runtime. Unfortunately, recommendation quality is unlikely to be
optimal because the algorithms are not aware of any social information that may
be available. Two proposed approaches take a more social view on tag
recommendation regarding the issue: social contact variants and social groups
of interest. The user data is varied and used as a source of associations. The
adoption of social contact variants has two approaches. The first social
variant is User-centered Knowledge, to contrast Collective Knowledge. It
improves tag recommendation by grouping historic tag data according to friend
relationships and interests. The second variant is dubbed 'social batched
personomy' and attempts to address both quality and scalability issues by
processing queries in batches instead of individually, such as done in a
conventional personomy approach. For the social group of interest, 'community
batched personomy' is proposed to provide better accuracy groups of
recommendation systems in contrast also to Collective Knowledge. By taking
social information into account can enhance the performance of recommendation
systems.Comment: 6 page
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