3,960 research outputs found
Geodesic-Preserving Polygon Simplification
Polygons are a paramount data structure in computational geometry. While the
complexity of many algorithms on simple polygons or polygons with holes depends
on the size of the input polygon, the intrinsic complexity of the problems
these algorithms solve is often related to the reflex vertices of the polygon.
In this paper, we give an easy-to-describe linear-time method to replace an
input polygon by a polygon such that (1)
contains , (2) has its reflex
vertices at the same positions as , and (3) the number of vertices
of is linear in the number of reflex vertices. Since the
solutions of numerous problems on polygons (including shortest paths, geodesic
hulls, separating point sets, and Voronoi diagrams) are equivalent for both
and , our algorithm can be used as a preprocessing
step for several algorithms and makes their running time dependent on the
number of reflex vertices rather than on the size of
A Polynomial-time Algorithm for Outerplanar Diameter Improvement
The Outerplanar Diameter Improvement problem asks, given a graph and an
integer , whether it is possible to add edges to in a way that the
resulting graph is outerplanar and has diameter at most . We provide a
dynamic programming algorithm that solves this problem in polynomial time.
Outerplanar Diameter Improvement demonstrates several structural analogues to
the celebrated and challenging Planar Diameter Improvement problem, where the
resulting graph should, instead, be planar. The complexity status of this
latter problem is open.Comment: 24 page
Survivability in Time-varying Networks
Time-varying graphs are a useful model for networks with dynamic connectivity
such as vehicular networks, yet, despite their great modeling power, many
important features of time-varying graphs are still poorly understood. In this
paper, we study the survivability properties of time-varying networks against
unpredictable interruptions. We first show that the traditional definition of
survivability is not effective in time-varying networks, and propose a new
survivability framework. To evaluate the survivability of time-varying networks
under the new framework, we propose two metrics that are analogous to MaxFlow
and MinCut in static networks. We show that some fundamental
survivability-related results such as Menger's Theorem only conditionally hold
in time-varying networks. Then we analyze the complexity of computing the
proposed metrics and develop several approximation algorithms. Finally, we
conduct trace-driven simulations to demonstrate the application of our
survivability framework to the robust design of a real-world bus communication
network
Evaluation MCDM Multi-disjoint Paths Selection Algorithms Using Fuzzy-Copeland Ranking Method
To increase the Internet's reliability and to have greater control over traffic transmission, reliable path selection is important and Multipath routing is promising technique that are used in the communication networks. Finding reliable end-end paths and backup can increase network performance. So, using proper decision metrics and algorithm should be used to paths and backup selection phase in these networks. For this goal, in this paper selecting a more reliable multi disjoint paths is addressed as a multi-criteria decision making (MCDM) problem and availability factor is defined and calculated based on network histories. For decision algorithm, a new fuzzy evaluation method is proposed to rank these multi disjoint paths selection algorithms and it is compared with bandwidth based, TOPSIS, FuzzyTOPSIS and AHP methods as candidate techniques to select more appropriate global disjoint paths in the IP/MPLS networks with packet loss, delay and availability parameters as decision making metrics. The proposed method combines fuzzy theory and Copeland method to evaluate the rank of each proposed method base on bandwidth, delay and new defined availability metric of selected end to end paths. Simulation results show that this method selects more reliable backup paths with better bandwidth in compared with others and can be used to path selection in IP/MPLS networks
Open sets satisfying systems of congruences
A famous result of Hausdorff states that a sphere with countably many points
removed can be partitioned into three pieces A,B,C such that A is congruent to
B (i.e., there is an isometry of the sphere which sends A to B), B is congruent
to C, and A is congruent to (B union C); this result was the precursor of the
Banach-Tarski paradox. Later, R. Robinson characterized the systems of
congruences like this which could be realized by partitions of the (entire)
sphere with rotations witnessing the congruences. The pieces involved were
nonmeasurable. In the present paper, we consider the problem of which systems
of congruences can be satisfied using open subsets of the sphere (or related
spaces); of course, these open sets cannot form a partition of the sphere, but
they can be required to cover "most of" the sphere in the sense that their
union is dense. Various versions of the problem arise, depending on whether one
uses all isometries of the sphere or restricts oneself to a free group of
rotations (the latter version generalizes to many other suitable spaces), or
whether one omits the requirement that the open sets have dense union, and so
on. While some cases of these problems are solved by simple geometrical
dissections, others involve complicated iterative constructions and/or results
from the theory of free groups. Many interesting questions remain open.Comment: 44 page
Notions of Connectivity in Overlay Networks
International audience" How well connected is the network? " This is one of the most fundamental questions one would ask when facing the challenge of designing a communication network. Three major notions of connectivity have been considered in the literature, but in the context of traditional (single-layer) networks, they turn out to be equivalent. This paper introduces a model for studying the three notions of connectivity in multi-layer networks. Using this model, it is easy to demonstrate that in multi-layer networks the three notions may differ dramatically. Unfortunately, in contrast to the single-layer case, where the values of the three connectivity notions can be computed efficiently, it has been recently shown in the context of WDM networks (results that can be easily translated to our model) that the values of two of these notions of connectivity are hard to compute or even approximate in multi-layer networks. The current paper shed some positive light into the multi-layer connectivity topic: we show that the value of the third connectivity notion can be computed in polynomial time and develop an approximation for the construction of well connected overlay networks
Link-Prediction Enhanced Consensus Clustering for Complex Networks
Many real networks that are inferred or collected from data are incomplete
due to missing edges. Missing edges can be inherent to the dataset (Facebook
friend links will never be complete) or the result of sampling (one may only
have access to a portion of the data). The consequence is that downstream
analyses that consume the network will often yield less accurate results than
if the edges were complete. Community detection algorithms, in particular,
often suffer when critical intra-community edges are missing. We propose a
novel consensus clustering algorithm to enhance community detection on
incomplete networks. Our framework utilizes existing community detection
algorithms that process networks imputed by our link prediction based
algorithm. The framework then merges their multiple outputs into a final
consensus output. On average our method boosts performance of existing
algorithms by 7% on artificial data and 17% on ego networks collected from
Facebook
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