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1,329
Digraphs  Theory, Algorithms and Applications
, 2007
"... Graph theory is a very popular area of discrete mathematics with not only numerous theoretical developments, but also countless applications to practical problems. As a research area, graph theory is still relatively young, but it is maturing rapidly with many deep results having been discovered o ..."
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Cited by 377 (48 self)
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over the last couple of decades. The theory of graphs can be roughly partitioned into two branches: the areas of undirected graphs and directed graphs (digraphs). Even though both areas have numerous important applications, for various reasons, undirected graphs have been studied much more extensively
Consensus Problems in Networks of Agents with Switching Topology and TimeDelays
, 2003
"... In this paper, we discuss consensus problems for a network of dynamic agents with fixed and switching topologies. We analyze three cases: i) networks with switching topology and no timedelays, ii) networks with fixed topology and communication timedelays, and iii) maxconsensus problems (or leader ..."
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Cited by 1112 (21 self)
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.e. algebraic connectivity of the network) and the negotiation speed (or performance) of the corresponding agreement protocol. It turns out that balanced digraphs play an important role in addressing averageconsensus problems. We introduce disagreement functions that play the role of Lyapunov functions
A Framework for Dynamic Graph Drawing
 CONGRESSUS NUMERANTIUM
, 1992
"... Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized as follows ..."
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Cited by 628 (44 self)
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Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized
Finding the k Shortest Paths
, 1997
"... We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m + n log n + k). We can also find the k shortest pat ..."
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Cited by 401 (2 self)
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We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m + n log n + k). We can also find the k shortest
Estimation and prediction for stochastic blockstructures.
 Journal of the American Statistical Association
, 2001
"... A statistical approach to a posteriori blockmodeling for digraphs and valued digraphs is proposed. The probability model assumes that the vertices of the digraph are partitioned into several unobserved (latent) classes and that the probability distribution of the relation between two vertices depen ..."
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Cited by 231 (5 self)
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A statistical approach to a posteriori blockmodeling for digraphs and valued digraphs is proposed. The probability model assumes that the vertices of the digraph are partitioned into several unobserved (latent) classes and that the probability distribution of the relation between two vertices
DBMSs on a modern processor: Where does time go
 in VLDB
, 1999
"... Recent highperformance processors employ sophisticated techniques to overlap and simultaneously execute multiple computation and memory operations. Intuitively, these techniques should help database applications, which are becoming increasingly compute and memory bound. Unfortunately, recent studie ..."
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Cited by 246 (26 self)
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this problem. However, to best design high performance DBMSs we must carefully evaluate and understand the processor and memory behavior of commercial DBMSs on today’s hardware platforms. In this paper we answer the question “Where does time go when a database system is executed on a modern computer platform
On Digraph Coloring Problems and Treewidth Duality
 20th IEEE Symposium on Logic in Computer Science (LICS
, 2005
"... It is known that every constraintsatisfaction problem (CSP) reduces, and is in fact polynomially equivalent, to a digraph coloring problem. By carefully analyzing the constructions, we observe that the reduction is quantifierfree. Using this, we illustrate the power of the logical approach to CSPs ..."
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Cited by 53 (2 self)
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It is known that every constraintsatisfaction problem (CSP) reduces, and is in fact polynomially equivalent, to a digraph coloring problem. By carefully analyzing the constructions, we observe that the reduction is quantifierfree. Using this, we illustrate the power of the logical approach to CSPs
Digraph decompositions and monotonicity in digraph searching
 CoRR
"... We consider Cops and Robber games on digraphs and their corresponding decompositions. In particular we show nonmonotonicity of two important variants of these games, namely the variants underlying DAG and Kellydecompositions. Furthermore we explore the limits of the algorithmic applicability of d ..."
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Cited by 16 (2 self)
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of digraph decompositions and show that various natural candidates for problems that might benefit from digraphs having small “directed width ” remain NPcomplete even on almost acyclic graphs. 1
Some parameterized problems on digraphs
 Comput. J
"... Abstract We survey known results on parameterized complexity of the feedback set problems for digraphs. We prove new results on some parameterizations of the paired comparison problems on digraphs. One of our theorems implies a new result for a parameterized version of the linear arrangement proble ..."
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Cited by 6 (2 self)
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Abstract We survey known results on parameterized complexity of the feedback set problems for digraphs. We prove new results on some parameterizations of the paired comparison problems on digraphs. One of our theorems implies a new result for a parameterized version of the linear arrangement
Approximating the Minimum Equivalent Digraph
, 1995
"... The minimum equivalent graph (MEG) problem is as follows: given a directed graph, find a smallest subset of the edges that maintains all teachability relations between nodes. This problem is NPhard; this paper gives an approximation algorithm achieving a performance guarantee of about 1.64 in poly ..."
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Cited by 42 (2 self)
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.64 in polynomial time. The algorithm achieves a performance guarantee of 1.75 in the time required for transitive closure. The heart of the MEG problem is the minimum strongly connected spanning subgraph (SCSS) problemthe MEG problem restricted to strongly connected digraphs. For the minimum SCSS problem
Results 1  10
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