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156
Propositional Circumscription and Extended Closed World Reasoning are $\Pi^P_2$complete
 Theoretical Computer Science
, 1993
"... Circumscription and the closed world assumption with its variants are wellknown nonmonotonic techniques for reasoning with incomplete knowledge. Their complexity in the propositional case has been studied in detail for fragments of propositional logic. One open problem is whether the deduction prob ..."
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Cited by 99 (22 self)
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Circumscription and the closed world assumption with its variants are wellknown nonmonotonic techniques for reasoning with incomplete knowledge. Their complexity in the propositional case has been studied in detail for fragments of propositional logic. One open problem is whether the deduction problem for arbitrary propositional theories under the extended closed world assumption or under circumscription is $\Pi^P_2$complete, i.e., complete for a class of the second level of the polynomial hierarchy. We answer this question by proving these problems $\Pi^P_2$complete, and we show how this result applies to other variants of closed world reasoning.
Automatic graph drawing and readability of diagrams
 IEEE Transactions on Systems, Man and Cybernetics
, 1988
"... AhtractDiagrams are widely used in several areas of computer wience, and their effectiveness is thoroughly recognized. One of the main qualities requested for them is readability; this is especially, but not exclusively, true in the area of information systems, where diagrams are used to model data ..."
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Cited by 91 (8 self)
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AhtractDiagrams are widely used in several areas of computer wience, and their effectiveness is thoroughly recognized. One of the main qualities requested for them is readability; this is especially, but not exclusively, true in the area of information systems, where diagrams are used to model data and functions of the application. Up to now, diagrams have been produced manually or with the aid of a graphic editor; in both caws placement of symbols and routing of connections are under responsibility of the designer. The goal of the work is to investigate how readability of diagrams can be achieved by means of automatic tools. Existing results in the literature are compared, and a comprehensive algorithmic approach to the problem is proposed. The algorithm presented draws graphs on a grid and is suitable for both undirected graphs and mixed graphs that contain as subgraphs hierarchic structures. Finally, several applications of a graphic tool that embodies the aforementioned facility are shown. I.
The maximum edge biclique problem is NPcomplete
 Discrete Applied Mathematics
, 2000
"... We prove that the maximum edge biclique problem in bipartite graphs is NPcomplete. A biclique in a bipartite graph is a vertex induced subgraph which is complete. The problem of finding a biclique with a maximum number of vertices is known to be solvable in polynomial time but the complexity o ..."
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Cited by 88 (0 self)
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We prove that the maximum edge biclique problem in bipartite graphs is NPcomplete. A biclique in a bipartite graph is a vertex induced subgraph which is complete. The problem of finding a biclique with a maximum number of vertices is known to be solvable in polynomial time but the complexity of finding a biclique with a maximum number of edges was still undecided. 1 Introduction Let G =(V,E) be a graph with vertex set V and edge set E.Apairof two disjoint subsets A and B of V is called a biclique if {a, b}#E for all a # A and b # B.Thustheedges{a, b} form a complete bipartite subgraph of G (which is not necessarily an induced subgraph if G is not bipartite). A biclique {A, B} clearly has A + B vertices and A#B edges. In this note we restrict ourselves to case that G is bipartite. The two colour classes of G will be denoted by V 1 and V 2 ,soV = V 1 # V 2 . Already in the book of Garey and Johnson [2] (problem GT24) the complexity of deciding whether or not a bipartit...
Biconnectivity Approximations and Graph Carvings
, 1994
"... A spanning tree in a graph is the smallest connected spanning subgraph. Given a graph, how does one find the smallest (i.e., least number of edges) 2connected spanning subgraph (connectivity refers to both edge and vertex connectivity, if not specified) ? Unfortunately, the problem is known to be ..."
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Cited by 82 (3 self)
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A spanning tree in a graph is the smallest connected spanning subgraph. Given a graph, how does one find the smallest (i.e., least number of edges) 2connected spanning subgraph (connectivity refers to both edge and vertex connectivity, if not specified) ? Unfortunately, the problem is known to be NP hard. We consider the problem of finding a better approximation to the smallest 2connected subgraph, by an efficient algorithm. For 2edge connectivity our algorithm guarantees a solution that is no more than 3 2 times the optimal. For 2vertex connectivity our algorithm guarantees a solution that is no more than 5 3 times the optimal. The previous best approximation factor is 2 for each of these problems. The new algorithms (and their analyses) depend upon a structure called a carving of a graph, which is of independent interest. We show that approximating the optimal solution to within an additive constant is NP hard as well. We also consider the case where the graph has edge weigh...
Models and Approximation Algorithms for Channel Assignment in Radio Networks
, 2000
"... We consider the frequency assignment (broadcast scheduling) problem for packet radio networks. Such networks are naturally modeled by graphs with a certain geometric structure. The problem of broadcast scheduling can be cast as a variant of the vertex coloring problem (called the distance2 coloring ..."
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Cited by 73 (3 self)
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We consider the frequency assignment (broadcast scheduling) problem for packet radio networks. Such networks are naturally modeled by graphs with a certain geometric structure. The problem of broadcast scheduling can be cast as a variant of the vertex coloring problem (called the distance2 coloring problem) on the graph that models a given packet radio network. We present efficient approximation algorithms for the distance2 coloring problem for various geometric graphs including those that naturally model a large class of packet radio networks. The class of graphs considered include (r, s)civilized graphs, planar graphs, graphs with bounded genus, etc.
Replicator Equations, Maximal Cliques, and Graph Isomorphism
, 1999
"... We present a new energyminimization framework for the graph isomorphism problem that is based on an equivalent maximum clique formulation. The approach is centered around a fundamental result proved by Motzkin and Straus in the mid1960s, and recently expanded in various ways, which allows us to fo ..."
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Cited by 52 (11 self)
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We present a new energyminimization framework for the graph isomorphism problem that is based on an equivalent maximum clique formulation. The approach is centered around a fundamental result proved by Motzkin and Straus in the mid1960s, and recently expanded in various ways, which allows us to formulate the maximum clique problem in terms of a standard quadratic program. The attractive feature of this formulation is that a clear onetoone correspondence exists between the solutions of the quadratic program and those in the original, combinatorial problem. To solve the program we use the socalled replicator equations—a class of straightforward continuous and discretetime dynamical systems developed in various branches of theoretical biology. We show how, despite their inherent inability to escape from local solutions, they nevertheless provide experimental results that are competitive with those obtained using more elaborate meanfield annealing heuristics.
Estimation of Power Dissipation in CMOS Combinational Circuits Using Boolean Function Manipulation
, 1992
"... Estimating maximum power dissipation for a CMOS logic network is difficult because the power dissipated by the network is typically a strong function of the network's inputs. This implies that the number of simulations which must be performed in order to find the maximum power dissipation is exponen ..."
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Cited by 50 (0 self)
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Estimating maximum power dissipation for a CMOS logic network is difficult because the power dissipated by the network is typically a strong function of the network's inputs. This implies that the number of simulations which must be performed in order to find the maximum power dissipation is exponential in the number of inputs to the network. In this paper we show that a simplified model of power dissipation relates maximizing dissipation to maximizing gate output activity, appropriately weighted to account for differing load capacitances. To find the input or input sequence that maximizes the weighted activity, we give algorithms for transforming the problem to a weighted rnaxsatisfiability problem, and then present exact and approximate algorithms for solving weighted maxsatisfiability. Algorithms for constructing the maxsatisfiability problem for both dynamic and static CMOS, where for the latter dissipation caused by glitching is considered, are presented. Also, we present efficient exact and approximate methods for solving weighted maxsatlsfiability and show that these methods are viable for largescale problems through examination of experimental results.
Graph Sandwich Problems
, 1994
"... The graph sandwich problem for property \Pi is defined as follows: Given two graphs G ) such that E ` E , is there a graph G = (V; E) such that E which satisfies property \Pi? Such problems generalize recognition problems and arise in various applications. Concentrating mainly o ..."
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Cited by 48 (8 self)
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The graph sandwich problem for property \Pi is defined as follows: Given two graphs G ) such that E ` E , is there a graph G = (V; E) such that E which satisfies property \Pi? Such problems generalize recognition problems and arise in various applications. Concentrating mainly on properties characterizing subfamilies of perfect graphs, we give polynomial algorithms for several properties and prove the NPcompleteness of others. We describe
DegreeConstrained Multicasting in PointtoPoint Networks
 in Proc. IEEE INFOCOM
, 1995
"... Establishing a multicast tree in a pointtopoint network of switch nodes, such as a widearea ATM network, is often modeled as the NPcomplete Steiner problem in networks. In this paper, we study algorithms for finding efficient multicast trees in the presence of constraints on the copying ability ..."
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Cited by 44 (4 self)
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Establishing a multicast tree in a pointtopoint network of switch nodes, such as a widearea ATM network, is often modeled as the NPcomplete Steiner problem in networks. In this paper, we study algorithms for finding efficient multicast trees in the presence of constraints on the copying ability of the individual switch nodes in the network. We refer to this problem as the degreeconstrained multicast tree problem and model it as the degreeconstrained Steiner problem in networks. Steiner heuristics for the degreeconstrained case are proposed and their simulation results for sparse, pointtopoint networks are presented. The results are compared with respect to their quality of solution, cost (running time), and the number of test cases for which no solution could be found. The results of our research indicate that efficient multicast trees can be found in large, sparse networks with small multicast groups even with limited multicast capability in the individual switches. Some of ...