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66
Network Coding in Undirected Networks
, 2004
"... Recent work in network coding shows that, it is necessary to consider both the routing and coding strategies to achieve optimal throughput of information transmission in data networks. So far, most research on network coding has focused on the model of directed networks, where each communication li ..."
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Cited by 69 (13 self)
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Recent work in network coding shows that, it is necessary to consider both the routing and coding strategies to achieve optimal throughput of information transmission in data networks. So far, most research on network coding has focused on the model of directed networks, where each communication link has a fixed direction. In this paper, we study the benefits of network coding in undirected networks, where each communication link is bidirectional. Our theoretical results show that, for a single unicast or broadcast session, there are no improvements with respect to throughput due to network coding. In the case of a single multicast session, such an improvement is bounded by a factor of two, as long as half integer routing is permitted. This is dramatically different from previous results obtained in directed networks. We also show that multicast throughput in an undirected network is independent of the selection of the sender within the multicast group. We finally show that, rather than improving the optimal achievable throughput, the benefit of network coding is to significantly facilitate the design of efficient algorithms to compute and achieve such optimal throughput. I.
A DomainSpecific Visual Language for Domain Model Evolution
 Journal of Visual Languages and Computing
, 2004
"... Domainspecific visual languages (DSVLs) are concise and useful tools that allow the rapid development of the behavior and/or structure of applications in welldefined domains. These languages are typically developed specifically for a domain, and have a strong cohesion to the domain concepts, which ..."
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Cited by 31 (5 self)
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Domainspecific visual languages (DSVLs) are concise and useful tools that allow the rapid development of the behavior and/or structure of applications in welldefined domains. These languages are typically developed specifically for a domain, and have a strong cohesion to the domain concepts, which often appear as primitives in the language. The strong cohesion between DSVL language primitives and the domain is a benefit for development by domain experts, but can be a drawback when the domain evolves – even when that evolution appears insignificant. This paper presents a domainspecific visual language developed expressly for the evolution of domainspecific visual languages, and uses concepts from graphrewriting to specify and carry out the transformation of the models built using the original DSVL. 1.
Properly colored subgraphs and rainbow subgraphs in edgecolorings with local constraints
 ALGORITHMS
, 2003
"... We consider a canonical Ramsey type problem. An edgecoloring of a graph is called mgood if each color appears at most m times at each vertex. Fixing a graph G and a positive integer m, let f(m, G) denote the smallest n such that every mgood edgecoloring of K n yields a properly edgecolored ..."
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Cited by 20 (0 self)
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We consider a canonical Ramsey type problem. An edgecoloring of a graph is called mgood if each color appears at most m times at each vertex. Fixing a graph G and a positive integer m, let f(m, G) denote the smallest n such that every mgood edgecoloring of K n yields a properly edgecolored copy of G, and let g(m, G) denote the smallest n such that every mgood edgecoloring of K n yields a rainbow copy of G. We give bounds on f(m, G) and g(m, G). For complete graphs G � K t, we have c 1mt 2 /ln t � f(m, K t) � c 2mt 2, and c � 1mt 3 /ln t � g(m, K t) � c � 2mt 3 /ln t, where c 1, c 2, c � 1, c � 2 are absolute constants. We also give bounds on f(m, G) and g(m, G) for general graphs G in terms of degrees in G. In particular, we show that for fixed m and d, and all sufficiently large n compared to m and d, f(m, G) � n for all graphs G with n vertices and
Metamodel driven model migration
 Vanderbilt University
, 2003
"... I love you, and I’m proud of you too. Thanks for being here for me. Jon iii ACKNOWLEDGEMENTS I give many thanks to my advisor, Dr. Gabor Karsai for being the Best AllAround Advisor™. Gabor, without your excellent teaching skills and motivational abilities, I would not be in the position I am today. ..."
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Cited by 16 (3 self)
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I love you, and I’m proud of you too. Thanks for being here for me. Jon iii ACKNOWLEDGEMENTS I give many thanks to my advisor, Dr. Gabor Karsai for being the Best AllAround Advisor™. Gabor, without your excellent teaching skills and motivational abilities, I would not be in the position I am today. Vanderbilt is lucky to have you, as will be any other student under your tutelage. I also thank very heartily the other members of my committee. Dr. Janos Sztipanovits, for his political insight (and vision for my future career); Dr. Akos Ledeczi, for holding my feet to the fire when it comes to sticking up for the value of my research, and also social interactions within ISIS; Dr. Greg Nordstrom, for (as usual) providing valuable comments in the discussion of all things metamodeling related, not to mention being an allaround good guy to bounce ideas allaround with; and of course Dr. Doug
A novel spectral coding in a large graph database
 In Proceedings of the International Conference on Extending Database Technology
, 2008
"... Retrieving related graphs containing a query graph from a large graph database is a key issue in many graphbased applications, such as drug discovery and structural pattern recognition. Because subgraph isomorphism is a NPcomplete problem [4], we have to employ a filterandverification framework ..."
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Cited by 15 (2 self)
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Retrieving related graphs containing a query graph from a large graph database is a key issue in many graphbased applications, such as drug discovery and structural pattern recognition. Because subgraph isomorphism is a NPcomplete problem [4], we have to employ a filterandverification framework to speed up the search efficiency, that is, using an effective and efficient pruning strategy to filter out the false positives (graphs that are not possible in the results) as many as possible first, then validating the remaining candidates by subgraph isomorphism checking. In this paper, we propose a novel filtering method, a spectral encoding method, i.e. GCoding. Specifically, we assign a signature to each vertex based on its local structures. Then, we generate a spectral graph code by combining all vertex signatures in a graph. Based on spectral graph codes, we derive a necessary condition for subgraph isomorphism. Then we propose two pruning rules for subgraph search problem, and prove that they satisfy the nofalsenegative requirement (no dismissal in answers). Since graph codes are in numerical space, we take this advantage and conduct efficient filtering over graph codes. Extensive experiments show that GCoding outperforms existing counterpart methods. 1.
THE FREQUENCY SPACE OF A FREE GROUP
, 2003
"... We analyze the structure of the frequency space Q ∞ of a free group Fk consisting of all shiftinvariant Borel probability measures on ∂Fk and study the natural action of Out(Fk) on Q∞. In particular we prove that for any outer automorphism φ of Fk the conjugacy distortion spectrum of φ, consisting ..."
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Cited by 14 (9 self)
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We analyze the structure of the frequency space Q ∞ of a free group Fk consisting of all shiftinvariant Borel probability measures on ∂Fk and study the natural action of Out(Fk) on Q∞. In particular we prove that for any outer automorphism φ of Fk the conjugacy distortion spectrum of φ, consisting of all numbers φ(w)/w, where w is a nontrivial conjugacy class, is a convex subset of Q.
Symmetric ILP: coloring and small integers
 Discrete Optimization
"... This Article is brought to you for free and open access by Research Showcase. It has been accepted for inclusion in Tepper School of Business by an ..."
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Cited by 6 (0 self)
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This Article is brought to you for free and open access by Research Showcase. It has been accepted for inclusion in Tepper School of Business by an
The circular chromatic index of graphs of high girth
 J. COMBIN. TH. (B
"... We show that for each ε>0 and each integer ∆ ≥ 1, there exists a number g such that for any graph G of maximum degree ∆ and girth at least g, the circular chromatic index of G is at most ∆ + ε. ..."
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Cited by 5 (2 self)
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We show that for each ε>0 and each integer ∆ ≥ 1, there exists a number g such that for any graph G of maximum degree ∆ and girth at least g, the circular chromatic index of G is at most ∆ + ε.