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Acyclic Graphs
"... of RAM, etc. DPTs solve this by performing parallel searches on different trees, then consolidating the results at the client side. We investigate how lookups can be made more scalable and efficient. In this paper, we propose a prefixbased lookup mechanism using a trie structure. In particular, we p ..."
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of RAM, etc. DPTs solve this by performing parallel searches on different trees, then consolidating the results at the client side. We investigate how lookups can be made more scalable and efficient. In this paper, we propose a prefixbased lookup mechanism using a trie structure. In particular, we present two main contributions: (a) the DPG data structure which offers improved lookup performance over the Dynamic Prefix Tree (DPT) [3] by reducing the number of hops during node traversal; and (b) an lexical encoding scheme that allows numeric properties to be handled. With this encoding scheme, range queries with numeric properties require less messages as requests are sent to those nodes that are pertinent to the search.
Partition Coefficients of Acyclic Graphs
 Proc. WG 95, GraphTheoretic Concepts in Computer Science, Lecture Notes in Comp. Sci., #1017
, 1995
"... . We develop the concept of a "closure space" which appears with different names in many aspects of graph theory. We show that acyclic graphs can be almost characterized by the partition coefficients of their associated closure spaces. The resulting nearly total ordering of all acyclic ..."
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. We develop the concept of a "closure space" which appears with different names in many aspects of graph theory. We show that acyclic graphs can be almost characterized by the partition coefficients of their associated closure spaces. The resulting nearly total ordering of all
Generic Directed Acyclic Graphs
"... Generic algorithms are algorithms using abstract data types. Multiple generic algorithms can be linked together in a directed acyclic graph (generic DAG) so that more complex generic algorithms can be formed. Views describe relationships between dierent data types. By compilation, specialized generi ..."
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Generic algorithms are algorithms using abstract data types. Multiple generic algorithms can be linked together in a directed acyclic graph (generic DAG) so that more complex generic algorithms can be formed. Views describe relationships between dierent data types. By compilation, specialized
ON THE LAPLACIAN COEFFICIENTS OF ACYCLIC GRAPHS
, 2006
"... Let G be a graph of order n and let Λ(G, λ) = ∑ n k=0 (−1)k ckλ n−k be the characteristic polynomial of its Laplacian matrix. Zhou and Gutman recently proved that among all trees of order n, the kth coefficient ck is largest when the tree is a path, and is smallest for stars. A new proof and a str ..."
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Cited by 6 (0 self)
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Let G be a graph of order n and let Λ(G, λ) = ∑ n k=0 (−1)k ckλ n−k be the characteristic polynomial of its Laplacian matrix. Zhou and Gutman recently proved that among all trees of order n, the kth coefficient ck is largest when the tree is a path, and is smallest for stars. A new proof and a
Path hitting in acyclic graphs
 In Proceedings of the 14th Annual European Symposium on Algorithms
, 2006
"... Abstract. An instance of the path hitting problem consists of two families of paths, D and H, in a common undirected graph, where each path in H is associated with a nonnegative cost. We refer to D and H as the sets of demand and hitting paths, respectively. When p ∈ H and q ∈ D share at least one ..."
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Cited by 6 (1 self)
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Abstract. An instance of the path hitting problem consists of two families of paths, D and H, in a common undirected graph, where each path in H is associated with a nonnegative cost. We refer to D and H as the sets of demand and hitting paths, respectively. When p ∈ H and q ∈ D share at least one
The algebra of directed acyclic graphs
 In Abramsky Festschrift, volume 7860 of LNCS
, 2013
"... ar ..."
On counting homomorphisms to directed acyclic graphs
 ICALP (1). Volume 4051 of Lecture Notes in Computer Science
, 2006
"... It is known that if P and NP are different then there is an infinite hierarchy of different complexity classes which lie strictly between them. Thus, if P ≠ NP, it is not possible to classify NP using any finite collection of complexity classes. This situation has led to attempts to identify smaller ..."
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Cited by 28 (4 self)
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. Graph homomorphism problems are a fertile setting in which to explore dichotomy theorems. Indeed, Feder and Vardi have shown that a dichotomy theorem for the problem of deciding whether there is a homomorphism to a fixed directed acyclic graph would resolve their longstanding dichotomy conjecture
RankBased Simulation on Acyclic Graphs
"... Abstract. The simulation preorder is widely used both as a behavioral relation in concurrent systems, and as an abstraction tool to reduce the state space in model checking, were memory requirement is clearly a critical issue. Therefore, in this context a simulation algorithm should address both tim ..."
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time and space efficiency. In this paper, we rely on the notion of rank to design an efficient simulation algorithm. It turns out that such algorithm outperforms—both in terms of time and in terms of space—the best simulation algorithms in the literature, on the class of acyclic graphs. 1
Multistate Directed Acyclic Graphs
 In Proc. Canadian AI
, 2007
"... Abstract. This paper continues the line of research on the representation and compilation of propositional knowledge bases with propositional directed acyclic graphs (PDAG), negation normal forms (NNF), and binary decision diagrams (BDD). The idea is to permit variables with more than two states and ..."
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Cited by 9 (3 self)
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Abstract. This paper continues the line of research on the representation and compilation of propositional knowledge bases with propositional directed acyclic graphs (PDAG), negation normal forms (NNF), and binary decision diagrams (BDD). The idea is to permit variables with more than two states
LCA queries in directed acyclic graphs
 In Proceedings of the 32nd ICALP, Lecture Notes in Computer Science 3580
, 2005
"... Abstract. We present two methods for finding a lowest common ancestor (LCA) for each pair of vertices of a directed acyclic graph (dag) on n vertices and m edges. The first method is surprisingly natural and solves the allpairs LCA problem for the input dag on n vertices and m edges in time O(nm). ..."
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Cited by 18 (2 self)
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Abstract. We present two methods for finding a lowest common ancestor (LCA) for each pair of vertices of a directed acyclic graph (dag) on n vertices and m edges. The first method is surprisingly natural and solves the allpairs LCA problem for the input dag on n vertices and m edges in time O
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