58,040 research outputs found
On the graph condition regarding the -inverse cover problem
In their paper titled "On -inverse covers of inverse monoids", Auinger and
Szendrei have shown that every finite inverse monoid has an -inverse cover
if and only if each finite graph admits a locally finite group variety with a
certain property. We study this property and prove that the class of graphs for
which a given group variety has the required property is closed downwards in
the minor ordering, and can therefore be described by forbidden minors. We find
these forbidden minors for all varieties of Abelian groups, thus describing the
graphs for which such a group variety satisfies the above mentioned condition
Convexities related to path properties on graphs; a unified approach
Path properties, such as 'geodesic', 'induced', 'all paths' define a convexity on a connected graph. The general notion of path property, introduced in this paper, gives rise to a comprehensive survey of results obtained by different authors for a variety of path properties, together with a number of new results. We pay special attention to convexities defined by path properties on graph products and the classical convexity invariants, such as the Caratheodory, Helly and Radon numbers in relation with graph invariants, such as clique numbers and other graph properties.
Hierarchical path-finding for Navigation Meshes (HNA*)
Path-finding can become an important bottleneck as both the size of the virtual environments and the number of agents navigating them increase. It is important to develop techniques that can be efficiently applied to any environment independently of its abstract representation. In this paper we present a hierarchical NavMesh representation to speed up path-finding. Hierarchical path-finding (HPA*) has been successfully applied to regular grids, but there is a need to extend the benefits of this method to polygonal navigation meshes. As opposed to regular grids, navigation meshes offer representations with higher accuracy regarding the underlying geometry, while containing a smaller number of cells. Therefore, we present a bottom-up method to create a hierarchical representation based on a multilevel k-way partitioning algorithm (MLkP), annotated with sub-paths that can be accessed online by our Hierarchical NavMesh Path-finding algorithm (HNA*). The algorithm benefits from searching in graphs with a much smaller number of cells, thus performing up to 7.7 times faster than traditional A¿ over the initial NavMesh. We present results of HNA* over a variety of scenarios and discuss the benefits of the algorithm together with areas for improvement.Peer ReviewedPostprint (author's final draft
Polynomial Invariants for Affine Programs
We exhibit an algorithm to compute the strongest polynomial (or algebraic)
invariants that hold at each location of a given affine program (i.e., a
program having only non-deterministic (as opposed to conditional) branching and
all of whose assignments are given by affine expressions). Our main tool is an
algebraic result of independent interest: given a finite set of rational square
matrices of the same dimension, we show how to compute the Zariski closure of
the semigroup that they generate
Communicability Angles Reveal Critical Edges for Network Consensus Dynamics
We consider the question of determining how the topological structure
influences a consensus dynamical process taking place on a network. By
considering a large dataset of real-world networks we first determine that the
removal of edges according to their communicability angle -an angle between
position vectors of the nodes in an Euclidean communicability space- increases
the average time of consensus by a factor of 5.68 in real-world networks. The
edge betweenness centrality also identifies -in a smaller proportion- those
critical edges for the consensus dynamics, i.e., its removal increases the time
of consensus by a factor of 3.70. We justify theoretically these findings on
the basis of the role played by the algebraic connectivity and the
isoperimetric number of networks on the dynamical process studied, and their
connections with the properties mentioned before. Finally, we study the role
played by global topological parameters of networks on the consensus dynamics.
We determine that the network density and the average distance-sum -an
analogous of the node degree for shortest-path distances, account for more than
80% of the variance of the average time of consensus in the real-world networks
studied.Comment: 15 pages, 2 figure
HitFraud: A Broad Learning Approach for Collective Fraud Detection in Heterogeneous Information Networks
On electronic game platforms, different payment transactions have different
levels of risk. Risk is generally higher for digital goods in e-commerce.
However, it differs based on product and its popularity, the offer type
(packaged game, virtual currency to a game or subscription service), storefront
and geography. Existing fraud policies and models make decisions independently
for each transaction based on transaction attributes, payment velocities, user
characteristics, and other relevant information. However, suspicious
transactions may still evade detection and hence we propose a broad learning
approach leveraging a graph based perspective to uncover relationships among
suspicious transactions, i.e., inter-transaction dependency. Our focus is to
detect suspicious transactions by capturing common fraudulent behaviors that
would not be considered suspicious when being considered in isolation. In this
paper, we present HitFraud that leverages heterogeneous information networks
for collective fraud detection by exploring correlated and fast evolving
fraudulent behaviors. First, a heterogeneous information network is designed to
link entities of interest in the transaction database via different semantics.
Then, graph based features are efficiently discovered from the network
exploiting the concept of meta-paths, and decisions on frauds are made
collectively on test instances. Experiments on real-world payment transaction
data from Electronic Arts demonstrate that the prediction performance is
effectively boosted by HitFraud with fast convergence where the computation of
meta-path based features is largely optimized. Notably, recall can be improved
up to 7.93% and F-score 4.62% compared to baselines.Comment: ICDM 201
Acyclic edge-coloring using entropy compression
An edge-coloring of a graph G is acyclic if it is a proper edge-coloring of G
and every cycle contains at least three colors. We prove that every graph with
maximum degree Delta has an acyclic edge-coloring with at most 4 Delta - 4
colors, improving the previous bound of 9.62 (Delta - 1). Our bound results
from the analysis of a very simple randomised procedure using the so-called
entropy compression method. We show that the expected running time of the
procedure is O(mn Delta^2 log Delta), where n and m are the number of vertices
and edges of G. Such a randomised procedure running in expected polynomial time
was only known to exist in the case where at least 16 Delta colors were
available. Our aim here is to make a pedagogic tutorial on how to use these
ideas to analyse a broad range of graph coloring problems. As an application,
also show that every graph with maximum degree Delta has a star coloring with 2
sqrt(2) Delta^{3/2} + Delta colors.Comment: 13 pages, revised versio
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