191 research outputs found
Community Detection via Semi-Synchronous Label Propagation Algorithms
A recently introduced novel community detection strategy is based on a label
propagation algorithm (LPA) which uses the diffusion of information in the
network to identify communities. Studies of LPAs showed that the strategy is
effective in finding a good community structure. Label propagation step can be
performed in parallel on all nodes (synchronous model) or sequentially
(asynchronous model); both models present some drawback, e.g., algorithm
termination is nor granted in the first case, performances can be worst in the
second case. In this paper, we present a semi-synchronous version of LPA which
aims to combine the advantages of both synchronous and asynchronous models. We
prove that our models always converge to a stable labeling. Moreover, we
experimentally investigate the effectiveness of the proposed strategy comparing
its performance with the asynchronous model both in terms of quality,
efficiency and stability. Tests show that the proposed protocol does not harm
the quality of the partitioning. Moreover it is quite efficient; each
propagation step is extremely parallelizable and it is more stable than the
asynchronous model, thanks to the fact that only a small amount of
randomization is used by our proposal.Comment: In Proc. of The International Workshop on Business Applications of
Social Network Analysis (BASNA '10
Distance Degree Regular Graphs and Distance Degree Injective Graphs: An Overview
The distance d ( v , u ) from a vertex v of G to a vertex u is the length of shortest v to u path. The eccentricity e v of v is the distance to a farthest vertex from v . If d ( v , u ) = e ( v ) , ( u ≠v ) , we say that u is an eccentric vertex of v . The radius rad ( G ) is the minimum eccentricity of the vertices, whereas the diameter diam ( G ) is the maximum eccentricity. A vertex v is a central vertex if e ( v ) = r a d ( G ) , and a vertex is a peripheral vertex if e ( v ) = d i a m ( G ) . A graph is self-centered if every vertex has the same eccentricity; that is, r a d ( G ) = d i a m ( G ) . The distance degree sequence (dds) of a vertex v in a graph G = ( V , E ) is a list of the number of vertices at distance 1 , 2 , . . . . , e ( v ) in that order, where e ( v ) denotes the eccentricity of v in G . Thus, the sequence ( d i 0 , d i 1 , d i 2 , … , d i j , … ) is the distance degree sequence of the vertex v i in G where d i j denotes the number of vertices at distance j from v i . The concept of distance degree regular (DDR) graphs was introduced by Bloom et al., as the graphs for which all vertices have the same distance degree sequence. By definition, a DDR graph must be a regular graph, but a regular graph may not be DDR. A graph is distance degree injective (DDI) graph if no two vertices have the same distance degree sequence. DDI graphs are highly irregular, in comparison with the DDR graphs. In this paper we present an exhaustive review of the two concepts of DDR and DDI graphs. The paper starts with an insight into all distance related sequences and their applications. All the related open problems are listed
An FPT Algorithm for Spanning Trees with Few Branch Vertices Parameterized by Modular-Width
The minimum branch vertices spanning tree problem consists in finding a spanning tree T of an input graph G having the minimum number of branch vertices, that is, vertices of degree at least three in T. This NP-hard problem has been widely studied in the literature and has many important applications in network design and optimization. Algorithmic and combinatorial aspects of the problem have been extensively studied and its fixed parameter tractability has been recently considered. In this paper we focus on modular-width and show that the problem of finding a spanning tree with the minimum number of branch vertices is FPT with respect to this parameter
Speeding up Networks Mining via Neighborhood Diversity
Parameterized complexity was classically used to efficiently solve NP-hard problems for small values of a fixed parameter. Then it has also been used as a tool to speed up algorithms for tractable problems. Following this line of research, we design algorithms parameterized by neighborhood diversity (nd) for several graph theoretic problems in P (e.g., Maximum Matching, Triangle counting and listing, Girth and Global minimum vertex cut). Such problems are known to admit algorithms parameterized by modular-width (mw) and consequently - being the nd a "special case" of mw - by nd. However, the proposed novel algorithms allow to improve the computational complexity from a time O(f(mw)? n +m) - where n and m denote, respectively, the number of vertices and edges in the input graph - which is multiplicative in n to a time O(g(nd)+n +m) which is additive only in the size of the input
Influence Diffusion in Social Networks under Time Window Constraints
We study a combinatorial model of the spread of influence in networks that generalizes
existing schemata recently proposed in the literature. In our model, agents change
behaviours/opinions on the basis of information collected from their neighbours in a
time interval of bounded size whereas agents are assumed to have unbounded memory
in previously studied scenarios. In our mathematical framework, one is given a network
G = (V , E), an integer value t(v) for each node v ∈ V , and a time window size λ. The
goal is to determine a small set of nodes (target set) that influences the whole graph. The
spread of influence proceeds in rounds as follows: initially all nodes in the target set are
influenced; subsequently, in each round, any uninfluenced node v becomes influenced if
the number of its neighbours that have been influenced in the previous λ rounds is greater
than or equal to t(v). We prove that the problem of finding a minimum cardinality target
set that influences the whole network G is hard to approximate within a polylogarithmic
factor. On the positive side, we design exact polynomial time algorithms for paths, rings,
and tree
- …