6,313 research outputs found
Tight Lower Bounds for Greedy Routing in Higher-Dimensional Small-World Grids
We consider Kleinberg's celebrated small world graph model (Kleinberg, 2000),
in which a D-dimensional grid {0,...,n-1}^D is augmented with a constant number
of additional unidirectional edges leaving each node. These long range edges
are determined at random according to a probability distribution (the
augmenting distribution), which is the same for each node. Kleinberg suggested
using the inverse D-th power distribution, in which node v is the long range
contact of node u with a probability proportional to ||u-v||^(-D). He showed
that such an augmenting distribution allows to route a message efficiently in
the resulting random graph: The greedy algorithm, where in each intermediate
node the message travels over a link that brings the message closest to the
target w.r.t. the Manhattan distance, finds a path of expected length O(log^2
n) between any two nodes. In this paper we prove that greedy routing does not
perform asymptotically better for any uniform and isotropic augmenting
distribution, i.e., the probability that node u has a particular long range
contact v is independent of the labels of u and v and only a function of
||u-v||.
In order to obtain the result, we introduce a novel proof technique: We
define a budget game, in which a token travels over a game board, while the
player manages a "probability budget". In each round, the player bets part of
her remaining probability budget on step sizes. A step size is chosen at random
according to a probability distribution of the player's bet. The token then
makes progress as determined by the chosen step size, while some of the
player's bet is removed from her probability budget. We prove a tight lower
bound for such a budget game, and then obtain a lower bound for greedy routing
in the D-dimensional grid by a reduction
NextBestOnce: Achieving Polylog Routing despite Non-greedy Embeddings
Social Overlays suffer from high message delivery delays due to insufficient
routing strategies. Limiting connections to device pairs that are owned by
individuals with a mutual trust relationship in real life, they form topologies
restricted to a subgraph of the social network of their users. While
centralized, highly successful social networking services entail a complete
privacy loss of their users, Social Overlays at higher performance represent an
ideal private and censorship-resistant communication substrate for the same
purpose.
Routing in such restricted topologies is facilitated by embedding the social
graph into a metric space. Decentralized routing algorithms have up to date
mainly been analyzed under the assumption of a perfect lattice structure.
However, currently deployed embedding algorithms for privacy-preserving Social
Overlays cannot achieve a sufficiently accurate embedding and hence
conventional routing algorithms fail. Developing Social Overlays with
acceptable performance hence requires better models and enhanced algorithms,
which guarantee convergence in the presence of local optima with regard to the
distance to the target.
We suggest a model for Social Overlays that includes inaccurate embeddings
and arbitrary degree distributions. We further propose NextBestOnce, a routing
algorithm that can achieve polylog routing length despite local optima. We
provide analytical bounds on the performance of NextBestOnce assuming a
scale-free degree distribution, and furthermore show that its performance can
be improved by more than a constant factor when including Neighbor-of-Neighbor
information in the routing decisions.Comment: 23 pages, 2 figure
Adaptive Dynamics of Realistic Small-World Networks
Continuing in the steps of Jon Kleinberg's and others celebrated work on
decentralized search in small-world networks, we conduct an experimental
analysis of a dynamic algorithm that produces small-world networks. We find
that the algorithm adapts robustly to a wide variety of situations in realistic
geographic networks with synthetic test data and with real world data, even
when vertices are uneven and non-homogeneously distributed.
We investigate the same algorithm in the case where some vertices are more
popular destinations for searches than others, for example obeying power-laws.
We find that the algorithm adapts and adjusts the networks according to the
distributions, leading to improved performance. The ability of the dynamic
process to adapt and create small worlds in such diverse settings suggests a
possible mechanism by which such networks appear in nature
Adoption of vehicular ad hoc networking protocols by networked robots
This paper focuses on the utilization of wireless networking in the robotics domain. Many researchers have already equipped their robots with wireless communication capabilities, stimulated by the observation that multi-robot systems tend to have several advantages over their single-robot counterparts. Typically, this integration of wireless communication is tackled in a quite pragmatic manner, only a few authors presented novel Robotic Ad Hoc Network (RANET) protocols that were designed specifically with robotic use cases in mind. This is in sharp contrast with the domain of vehicular ad hoc networks (VANET). This observation is the starting point of this paper. If the results of previous efforts focusing on VANET protocols could be reused in the RANET domain, this could lead to rapid progress in the field of networked robots. To investigate this possibility, this paper provides a thorough overview of the related work in the domain of robotic and vehicular ad hoc networks. Based on this information, an exhaustive list of requirements is defined for both types. It is concluded that the most significant difference lies in the fact that VANET protocols are oriented towards low throughput messaging, while RANET protocols have to support high throughput media streaming as well. Although not always with equal importance, all other defined requirements are valid for both protocols. This leads to the conclusion that cross-fertilization between them is an appealing approach for future RANET research. To support such developments, this paper concludes with the definition of an appropriate working plan
Robotic Wireless Sensor Networks
In this chapter, we present a literature survey of an emerging, cutting-edge,
and multi-disciplinary field of research at the intersection of Robotics and
Wireless Sensor Networks (WSN) which we refer to as Robotic Wireless Sensor
Networks (RWSN). We define a RWSN as an autonomous networked multi-robot system
that aims to achieve certain sensing goals while meeting and maintaining
certain communication performance requirements, through cooperative control,
learning and adaptation. While both of the component areas, i.e., Robotics and
WSN, are very well-known and well-explored, there exist a whole set of new
opportunities and research directions at the intersection of these two fields
which are relatively or even completely unexplored. One such example would be
the use of a set of robotic routers to set up a temporary communication path
between a sender and a receiver that uses the controlled mobility to the
advantage of packet routing. We find that there exist only a limited number of
articles to be directly categorized as RWSN related works whereas there exist a
range of articles in the robotics and the WSN literature that are also relevant
to this new field of research. To connect the dots, we first identify the core
problems and research trends related to RWSN such as connectivity,
localization, routing, and robust flow of information. Next, we classify the
existing research on RWSN as well as the relevant state-of-the-arts from
robotics and WSN community according to the problems and trends identified in
the first step. Lastly, we analyze what is missing in the existing literature,
and identify topics that require more research attention in the future
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