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Sequential Elimination Graphs
"... A graph is chordal if it does not contain any induced cycle of size greater than three. An alternative characterization of chordal graphs is via a perfect elimination ordering, which is an ordering of the vertices such that, for each vertex v, the neighbors of v that occur later than v in the order ..."
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A graph is chordal if it does not contain any induced cycle of size greater than three. An alternative characterization of chordal graphs is via a perfect elimination ordering, which is an ordering of the vertices such that, for each vertex v, the neighbors of v that occur later than v in the ordering form a clique. Akcoglu et al [2] define an extension of chordal graphs whereby the neighbors of v that occur later than v in the elimination order have at most k independent vertices. We refer to such graphs as sequentially kindependent graphs. Clearly this extension of chordal graphs also extends the class of (k+1)clawfree graphs. We study properties of such families of graphs, and we show that several natural classes of graphs are sequentially kindependent for small k. In particular, any intersection graph of translates of a convex object in a two dimensional plane is a sequentially 3independent graph; furthermore, any planar graph is a sequentially 3independent graph. For any fixed constant k, we develop simple, polynomial time approximation algorithms for sequentially kindependent graphs with respect to several wellstudied NPcomplete problems based on this ksequentially independent ordering. Our generalized formulation unifies and extends several previously known results. We also consider other classes of sequential elimination graphs.
Mining TeraScale Graphs: Theory, engineering and discoveries
, 2012
"... component, inference, spectral graph analysis, eigensolver, tensor analysis, graph management, How do we find patterns and anomalies, on graphs with billions of nodes and edges, which do not fit in memory? How to use parallelism for such Tera or Petascale graphs? In this thesis, we propose PEGASUS ..."
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component, inference, spectral graph analysis, eigensolver, tensor analysis, graph management, How do we find patterns and anomalies, on graphs with billions of nodes and edges, which do not fit in memory? How to use parallelism for such Tera or Petascale graphs? In this thesis, we propose PEGASUS, a large scale graph mining system implemented on the top of the HADOOP platform, the open source version of MAPREDUCE. PEGASUS includes algorithms which help us spot patterns and anomalous behaviors in large graphs. PEGASUS enables the structure analysis on large graphs. We unify many different structure analysis algorithms, including the analysis on connected components, PageRank, and radius/diameter, into a general primitive called GIMV. GIMV is highly optimized, achieving good scaleup on the number of edges and available machines. We discover surprising patterns using GIMV, including the 7degrees of separation in one of the largest publicly available Web graphs, with 7 billion edges. PEGASUS also enables the inference and the spectral analysis on large graphs. We design an efficient distributed belief propagation algorithm which infer the states of unlabeled nodes
Noname manuscript No. (will be inserted by the editor) Improving TCP Performance over Optical BurstSwitched (OBS) Networks Using Forward Segment Redundancy
, 2011
"... Abstract Random contentions occur in optical burstswitched (OBS) networks because of oneway signaling and lack of optical buffers. These contentions can occur at low loads and are not necessarily an indication of congestion. The loss caused by them, however, causes TCP at the transport layer to re ..."
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Abstract Random contentions occur in optical burstswitched (OBS) networks because of oneway signaling and lack of optical buffers. These contentions can occur at low loads and are not necessarily an indication of congestion. The loss caused by them, however, causes TCP at the transport layer to reduce its send rate drastically, which is unnecessary and reduces overall performance. In this paper, we propose forward segment redundancy (FSR), a proactive technique to prevent data loss during random contentions in the optical core. With FSR, redundant TCP segments are appended to each burst at the edge and redundant burst segmentation (RBS) is implemented in the core so that when a contention occurs, primarily redundant data is dropped. We develop an analytical throughput model for TCP over OBS with FSR and perform extensive simulations. FSR is found to improve TCP’s performance by an order of magnitude at high loads and by over two times at lower loads.
Parameterized Algorithms for (r, l)Partization
, 2013
"... We consider the (r, l)Partization problem of finding a set of at most k vertices whose deletion results in a graph that can be partitioned into r independent sets and l cliques. Restricted to perfect graphs and split graphs, we describe sequacious fixedparameter tractability results for (r, 0)Par ..."
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We consider the (r, l)Partization problem of finding a set of at most k vertices whose deletion results in a graph that can be partitioned into r independent sets and l cliques. Restricted to perfect graphs and split graphs, we describe sequacious fixedparameter tractability results for (r, 0)Partization, parameterized by k and r. For (r, l)Partization where r + l = 2, we describe an O∗(2k) algorithm for perfect graphs. We then study the parameterized complexity hardness of a generalization of the Above Guarantee Vertex Cover by a reduction from (r, l)Partization.