1,108 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
Towards Scalable Network Delay Minimization
Reduction of end-to-end network delays is an optimization task with
applications in multiple domains. Low delays enable improved information flow
in social networks, quick spread of ideas in collaboration networks, low travel
times for vehicles on road networks and increased rate of packets in the case
of communication networks. Delay reduction can be achieved by both improving
the propagation capabilities of individual nodes and adding additional edges in
the network. One of the main challenges in such design problems is that the
effects of local changes are not independent, and as a consequence, there is a
combinatorial search-space of possible improvements. Thus, minimizing the
cumulative propagation delay requires novel scalable and data-driven
approaches.
In this paper, we consider the problem of network delay minimization via node
upgrades. Although the problem is NP-hard, we show that probabilistic
approximation for a restricted version can be obtained. We design scalable and
high-quality techniques for the general setting based on sampling and targeted
to different models of delay distribution. Our methods scale almost linearly
with the graph size and consistently outperform competitors in quality
Robust geometric forest routing with tunable load balancing
Although geometric routing is proposed as a memory-efficient alternative to traditional lookup-based routing and forwarding algorithms, it still lacks: i) adequate mechanisms to trade stretch against load balancing, and ii) robustness to cope with network topology change.
The main contribution of this paper involves the proposal of a family of routing schemes, called Forest Routing. These are based on the principles of geometric routing, adding flexibility in its load balancing characteristics. This is achieved by using an aggregation of greedy embeddings along with a configurable distance function. Incorporating link load information in the forwarding layer enables load balancing behavior while still attaining low path stretch. In addition, the proposed schemes are validated regarding their resilience towards network failures
Compact Routing on Internet-Like Graphs
The Thorup-Zwick (TZ) routing scheme is the first generic stretch-3 routing
scheme delivering a nearly optimal local memory upper bound. Using both direct
analysis and simulation, we calculate the stretch distribution of this routing
scheme on random graphs with power-law node degree distributions, . We find that the average stretch is very low and virtually
independent of . In particular, for the Internet interdomain graph,
, the average stretch is around 1.1, with up to 70% of paths
being shortest. As the network grows, the average stretch slowly decreases. The
routing table is very small, too. It is well below its upper bounds, and its
size is around 50 records for -node networks. Furthermore, we find that
both the average shortest path length (i.e. distance) and width of
the distance distribution observed in the real Internet inter-AS graph
have values that are very close to the minimums of the average stretch in the
- and -directions. This leads us to the discovery of a unique
critical quasi-stationary point of the average TZ stretch as a function of
and . The Internet distance distribution is located in a
close neighborhood of this point. This observation suggests the analytical
structure of the average stretch function may be an indirect indicator of some
hidden optimization criteria influencing the Internet's interdomain topology
evolution.Comment: 29 pages, 16 figure
Randomized Shortest Paths with Net Flows and Capacity Constraints
This work extends the randomized shortest paths (RSP) model by investigating
the net flow RSP and adding capacity constraints on edge flows. The standard
RSP is a model of movement, or spread, through a network interpolating between
a random-walk and a shortest-path behavior [30, 42, 49]. The framework assumes
a unit flow injected into a source node and collected from a target node with
flows minimizing the expected transportation cost, together with a relative
entropy regularization term. In this context, the present work first develops
the net flow RSP model considering that edge flows in opposite directions
neutralize each other (as in electric networks), and proposes an algorithm for
computing the expected routing costs between all pairs of nodes. This quantity
is called the net flow RSP dissimilarity measure between nodes. Experimental
comparisons on node clustering tasks indicate that the net flow RSP
dissimilarity is competitive with other state-of-the-art dissimilarities. In
the second part of the paper, it is shown how to introduce capacity constraints
on edge flows, and a procedure is developed to solve this constrained problem
by exploiting Lagrangian duality. These two extensions should improve
significantly the scope of applications of the RSP framework
On the fixed-parameter tractability of the maximum connectivity improvement problem
In the Maximum Connectivity Improvement (MCI) problem, we are given a
directed graph and an integer and we are asked to find new
edges to be added to in order to maximize the number of connected pairs of
vertices in the resulting graph. The MCI problem has been studied from the
approximation point of view. In this paper, we approach it from the
parameterized complexity perspective in the case of directed acyclic graphs. We
show several hardness and algorithmic results with respect to different natural
parameters. Our main result is that the problem is -hard for parameter
and it is FPT for parameters and , the matching number of
. We further characterize the MCI problem with respect to other
complementary parameters.Comment: 15 pages, 1 figur
Improving information centrality of a node in complex networks by adding edges
The problem of increasing the centrality of a network node arises in many
practical applications. In this paper, we study the optimization problem of
maximizing the information centrality of a given node in a network
with nodes and edges, by creating new edges incident to . Since
is the reciprocal of the sum of resistance distance
between and all nodes, we alternatively consider the problem of minimizing
by adding new edges linked to . We show that the
objective function is monotone and supermodular. We provide a simple greedy
algorithm with an approximation factor and
running time. To speed up the computation, we also present an
algorithm to compute -approximate
resistance distance after iteratively adding edges, the
running time of which is for any
, where the notation suppresses the factors. We experimentally demonstrate the effectiveness and
efficiency of our proposed algorithms.Comment: 7 pages, 2 figures, ijcai-201
Minimizing Hitting Time between Disparate Groups with Shortcut Edges
Structural bias or segregation of networks refers to situations where two or
more disparate groups are present in the network, so that the groups are highly
connected internally, but loosely connected to each other. In many cases it is
of interest to increase the connectivity of disparate groups so as to, e.g.,
minimize social friction, or expose individuals to diverse viewpoints. A
commonly-used mechanism for increasing the network connectivity is to add edge
shortcuts between pairs of nodes. In many applications of interest, edge
shortcuts typically translate to recommendations, e.g., what video to watch, or
what news article to read next. The problem of reducing structural bias or
segregation via edge shortcuts has recently been studied in the literature, and
random walks have been an essential tool for modeling navigation and
connectivity in the underlying networks. Existing methods, however, either do
not offer approximation guarantees, or engineer the objective so that it
satisfies certain desirable properties that simplify the optimization~task. In
this paper we address the problem of adding a given number of shortcut edges in
the network so as to directly minimize the average hitting time and the maximum
hitting time between two disparate groups. Our algorithm for minimizing average
hitting time is a greedy bicriteria that relies on supermodularity. In
contrast, maximum hitting time is not supermodular. Despite, we develop an
approximation algorithm for that objective as well, by leveraging connections
with average hitting time and the asymmetric k-center problem.Comment: To appear in KDD 202
- …