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The NPcompleteness column: an ongoing guide
 Journal of Algorithms
, 1985
"... This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co ..."
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Cited by 188 (0 self)
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This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co., New York, 1979 (hereinafter referred to as ‘‘[G&J]’’; previous columns will be referred to by their dates). A background equivalent to that provided by [G&J] is assumed, and, when appropriate, crossreferences will be given to that book and the list of problems (NPcomplete and harder) presented there. Readers who have results they would like mentioned (NPhardness, PSPACEhardness, polynomialtimesolvability, etc.) or open problems they would like publicized, should
Modular Decomposition and Transitive Orientation
, 1999
"... A module of an undirected graph is a set X of nodes such for each node x not in X, either every member of X is adjacent to x, or no member of X is adjacent to x. There is a canonical linearspace representation for the modules of a graph, called the modular decomposition. Closely related to modular ..."
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Cited by 87 (13 self)
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A module of an undirected graph is a set X of nodes such for each node x not in X, either every member of X is adjacent to x, or no member of X is adjacent to x. There is a canonical linearspace representation for the modules of a graph, called the modular decomposition. Closely related to modular decomposition is the transitive orientation problem, which is the problem of assigning a direction to each edge of a graph so that the resulting digraph is transitive. A graph is a comparability graph if such an assignment is possible. We give O(n +m) algorithms for modular decomposition and transitive orientation, where n and m are the number of vertices and edges of the graph. This gives linear time bounds for recognizing permutation graphs, maximum clique and minimum vertex coloring on comparability graphs, and other combinatorial problems on comparability graphs and their complements.
Dynamic and efficient key management for access hierarchies
 In Proceedings of the ACM Conference on Computer and Communications Security
, 2005
"... Hierarchies arise in the context of access control whenever the user population can be modeled as a set of partially ordered classes (represented as a directed graph). A user with access privileges for a class obtains access to objects stored at that class and all descendant classes in the hierarchy ..."
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Cited by 64 (8 self)
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Hierarchies arise in the context of access control whenever the user population can be modeled as a set of partially ordered classes (represented as a directed graph). A user with access privileges for a class obtains access to objects stored at that class and all descendant classes in the hierarchy. The problem of key management for such hierarchies then consists of assigning a key to each class in the hierarchy so that keys for descendant classes can be obtained via efficient key derivation. We propose a solution to this problem with the following properties: (1) the space complexity of the public information is the same as that of storing the hierarchy; (2) the private information at a class consists of a single key associated with that class; (3) updates (i.e., revocations and additions) are handled locally in the hierarchy; (4) the scheme is provably secure against collusion; and (5) each node can derive the key of any of its descendant with a number of symmetrickey operations bounded by the length of the path between the nodes. Whereas many previous schemes had some of these properties, ours is the first that satisfies all of them. The security of our scheme is based on pseudorandom functions, without reliance on the Random Oracle Model. 18 Portions of this work were supported by Grants IIS0325345 and CNS06274488 from the
Stack And Queue Layouts Of Directed Acyclic Graphs: Part I
, 1996
"... . Stack layouts and queue layouts of undirected graphs have been used to model problems in fault tolerant computing and in parallel process scheduling. However, problems in parallel process scheduling are more accurately modeled by stack and queue layouts of directed acyclic graphs (dags). A stack ..."
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Cited by 26 (3 self)
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. Stack layouts and queue layouts of undirected graphs have been used to model problems in fault tolerant computing and in parallel process scheduling. However, problems in parallel process scheduling are more accurately modeled by stack and queue layouts of directed acyclic graphs (dags). A stack layout of a dag is similar to a stack layout of an undirected graph, with the additional requirement that the nodes of the dag be in some topological order. A queue layout is defined in an analogous manner. The stacknumber (queuenumber) of a dag is the smallest number of stacks (queues) required for its stack layout (queue layout). In this paper, bounds are established on the stacknumber and queuenumber of two classes of dags: tree dags and unicyclic dags. In particular, any tree dag can be laid out in 1 stack and in at most 2 queues; and any unicyclic dag can be laid out in at most 2 stacks and in at most 2 queues. Forbidden subgraph characterizations of 1queue tree dags and 1queue cycle d...
Complexity Theoretic Hardness Results for Query Learning
 COMPUTATIONAL COMPLEXITY
, 1998
"... We investigate the complexity of learning for the wellstudied model in which the learning algorithm may ask membership and equivalence queries. While complexity theoretic techniques have previously been used to prove hardness results in various learning models, these techniques typically are no ..."
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Cited by 19 (5 self)
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We investigate the complexity of learning for the wellstudied model in which the learning algorithm may ask membership and equivalence queries. While complexity theoretic techniques have previously been used to prove hardness results in various learning models, these techniques typically are not strong enough to use when a learning algorithm may make membership queries. We develop a general technique for proving hardness results for learning with membership and equivalence queries (and for more general query models). We apply the technique to show that, assuming NP != coNP, no polynomialtime membership and (proper) equivalence query algorithms exist for exactly learning readthrice DNF formulas, unions of k 3 halfspaces over the Boolean domain, or some other related classes. Our hardness results are representation dependent, and do not preclude the existence of representation independent algorithms. The general
Stack And Queue Layouts Of Posets
 SIAM J. Discrete Math
, 1995
"... . The stacknumber (queuenumber) of a poset is defined as the stacknumber (queuenumber) of its Hasse diagram viewed as a directed acyclic graph. Upper bounds on the queuenumber of a poset are derived in terms of its jumpnumber, its length, its width, and the queuenumber of its covering graph. A lower ..."
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Cited by 19 (4 self)
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. The stacknumber (queuenumber) of a poset is defined as the stacknumber (queuenumber) of its Hasse diagram viewed as a directed acyclic graph. Upper bounds on the queuenumber of a poset are derived in terms of its jumpnumber, its length, its width, and the queuenumber of its covering graph. A lower bound of \Omega\Gamma p n) is shown for the queuenumber of the class of nelement planar posets. The queuenumber of a planar poset is shown to be within a small constant factor of its width. The stacknumber of nelement posets with planar covering graphs is shown to be \Theta(n). These results exhibit sharp differences between the stacknumber and queuenumber of posets as well as between the stacknumber (queuenumber) of a poset and the stacknumber (queuenumber) of its covering graph. Key words. poset, queue layout, stack layout, book embedding, Hasse diagram, jumpnumber AMS subject classifications. 05C99, 68R10, 94C15 1. Introduction. Stack and queue layouts of undirected graphs appear ...
KEY MANAGEMENT FOR NONTREE ACCESS HIERARCHIES
, 2006
"... Access hierarchies are useful in many applications and are modeled as a set of access classes organized by a partial order. A user who obtains access to a class in such a hierarchy is entitled to access objects stored at that class, as well as objects stored at its descendant classes. Efficient sche ..."
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Cited by 16 (7 self)
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Access hierarchies are useful in many applications and are modeled as a set of access classes organized by a partial order. A user who obtains access to a class in such a hierarchy is entitled to access objects stored at that class, as well as objects stored at its descendant classes. Efficient schemes for this framework assign only one key to a class and use key derivation to permit access to descendant classes. Ideally, the key derivation uses simple primitives such as cryptographic hash computations and modular additions. A straightforward key derivation time is then linear in the length of the path between the user’s class and the class of the object that the user wants to access. Recently, work presented in [2] has given an efficient solution that significantly lowers this key derivation time, while
Focusing versus intransitivity: geometrical aspects of coevolution
 Genetic and Evolutionary Computation  GECCO 2003, number 2724 in LNCS
, 2003
"... Abstract. Recently, a minimal domain dubbed the numbers game has been proposed to illustrate wellknown issues in coevolutionary dynamics. The domain permits controlled introduction of features like intransitivity, allowing researchers to understand failings of a coevolutionary algorithm in terms ..."
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Cited by 16 (7 self)
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Abstract. Recently, a minimal domain dubbed the numbers game has been proposed to illustrate wellknown issues in coevolutionary dynamics. The domain permits controlled introduction of features like intransitivity, allowing researchers to understand failings of a coevolutionary algorithm in terms of the domain. In this paper, we show theoretically that a large class of coevolution problems closely resemble this minimal domain. In particular, all the problems in this class can be embedded into an ordered, ndimensional Euclidean space, and so can be construed as greaterthan games. Thus, conclusions derived using the numbers game are more widely applicable than might be presumed. In light of this observation, we present a simple algorithm aimed at remedying focusing problems and relativism in the numbers game. With it we show empirically that, contrary to expectations, focusing in transitive games can be more troublesome for coevolutionary algorithms than intransitivity. Practitioners should therefore be just as wary of focusing issues in application domains. 1
Threshold graph limits and random threshold graphs
 In preparation
"... Abstract. We study the limit theory of large threshold graphs and apply this to a variety of models for random threshold graphs. The results give a nice set of examples for the emerging theory of graph limits. 1. ..."
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Cited by 16 (10 self)
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Abstract. We study the limit theory of large threshold graphs and apply this to a variety of models for random threshold graphs. The results give a nice set of examples for the emerging theory of graph limits. 1.
On the Geometric Separability of Boolean Functions
 Discrete Applied Mathematics
, 1995
"... We investigate the complexity of the MEMBERSHIP... ..."
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Cited by 15 (0 self)
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We investigate the complexity of the MEMBERSHIP...