Results 1  10
of
49
Efficient detection of determinacy races in Cilk programs
 In Proceedings of the Ninth Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA
, 1997
"... A parallel multithreaded program that is ostensibly deterministic ..."
Abstract

Cited by 49 (15 self)
 Add to MetaCart
A parallel multithreaded program that is ostensibly deterministic
The Steiner tree polytope and related polyhedra
, 1994
"... We consider the vertexweighted version of the undirected Steiner tree problem. In this problem, a cost is incurred both for the vertices and the edges present in the Steiner tree. We completely describe the associated polytope by linear inequalities when the underlying graph is seriesparallel. For ..."
Abstract

Cited by 27 (1 self)
 Add to MetaCart
We consider the vertexweighted version of the undirected Steiner tree problem. In this problem, a cost is incurred both for the vertices and the edges present in the Steiner tree. We completely describe the associated polytope by linear inequalities when the underlying graph is seriesparallel. For general graphs, this formulation can be interpreted as a (partial) extended formulation for the Steiner tree problem. By projecting this formulation, we obtain some very large classes of facetdefining valid inequalities for the Steiner tree polytope.
Network Topology and the Efficiency of Equilibrium
, 2002
"... Different kinds of networks, such as transportation, communication, computer, and supply networks, are susceptible to similar kinds of inefficiencies. These arise when congestion externalities make each user's cost depend on the other users' choices of routes. If each user chooses the least expensiv ..."
Abstract

Cited by 17 (4 self)
 Add to MetaCart
Different kinds of networks, such as transportation, communication, computer, and supply networks, are susceptible to similar kinds of inefficiencies. These arise when congestion externalities make each user's cost depend on the other users' choices of routes. If each user chooses the least expensive (e.g., fastest) route from the users' common point of origin to the common destination, the result may be inefficient in the sense that there is an alternative assignment of routes to users that reduces the costs of all users. However, this may happen only for certain kinds of network topologies. This paper gives several alternative characterizations of networks in which inefficiencies may occur. In particular, a necessary and sufficient condition for inefficiency is that one of several specific, simple networks is embedded in the network. Keywords: Congestion, network topology, Braess's paradox, transportation networks, Wardrop equilibrium. 2 1.
Symmetry in Network Congestion Games: Pure Equilibria and Anarchy Cost
 In Proc. of the 3rd Workshop on Approximation and Online Algorithms (WAOA ’05
, 2005
"... Abstract. We study computational and coordination efficiency issues of Nash equilibria in symmetric network congestion games. We first propose a simple and natural greedy method that computes a pure Nash equilibrium with respect to traffic congestion in a network. In this algorithm each user plays o ..."
Abstract

Cited by 17 (6 self)
 Add to MetaCart
Abstract. We study computational and coordination efficiency issues of Nash equilibria in symmetric network congestion games. We first propose a simple and natural greedy method that computes a pure Nash equilibrium with respect to traffic congestion in a network. In this algorithm each user plays only once and allocates her traffic to a path selected via a shortest path computation. We then show that this algorithm works for seriesparallel networks when users are identical or when users are of varying demands but have the same best response strategy for any initial network traffic. We also give constructions where the algorithm fails if either the above condition is violated (even for seriesparallel networks) or the network is not seriesparallel (even for identical users). Thus, we essentially indicate the limits of the applicability of this greedy approach. We also study the price of anarchy for the objective of maximum latency. We prove that for any network of m uniformly related links and log m for identical users, the price of anarchy is Θ( 1
Algorithmic Aspects of Symbolic Switch Network Analysis
 IEEE Trans. CAD/IC
, 1987
"... A network of switches controlled by Boolean variables can be represented as a system of Boolean equations. The solution of this system gives a symbolic description of the conducting paths in the network. Gaussian elimination provides an efficient technique for solving sparse systems of Boolean eq ..."
Abstract

Cited by 16 (5 self)
 Add to MetaCart
A network of switches controlled by Boolean variables can be represented as a system of Boolean equations. The solution of this system gives a symbolic description of the conducting paths in the network. Gaussian elimination provides an efficient technique for solving sparse systems of Boolean equations. For the class of networks that arise when analyzing digital metaloxide semiconductor (MOS) circuits, a simple pivot selection rule guarantees that most s switch networks encountered in practice can be solved with O(s) operations. When represented by a directed acyclic graph, the set of Boolean formulas generated by the analysis has total size bounded by the number of operations required by the Gaussian elimination. This paper presents the mathematical basis for systems of Boolean equations, their solution by Gaussian elimination, and data structures and algorithms for representing and manipulating Boolean formulas.
Optimal reduction of twoterminal directed acyclic graphs
 SIAM Journal on Computing
, 1992
"... Abstract. Algorithms for seriesparallel graphs can be extended to arbitrary twoterminal dags if node reductions are used along with series and parallel reductions. A node reduction contracts a vertex with unit indegree (outdegree) into its sole incoming (outgoing) neighbor. This paper gives an O ..."
Abstract

Cited by 14 (1 self)
 Add to MetaCart
Abstract. Algorithms for seriesparallel graphs can be extended to arbitrary twoterminal dags if node reductions are used along with series and parallel reductions. A node reduction contracts a vertex with unit indegree (outdegree) into its sole incoming (outgoing) neighbor. This paper gives an O(n2"5) algorithm for minimizing node reductions, based on vertex cover in a transitive auxiliary graph. Applications include the analysis of PERT networks, dynamic programming approaches to network problems, and network reliability. For NPhard problems one can obtain algorithms that are exponential only in the minimum number of node reductions rather than the number of vertices. This gives improvements if the underlying graph is nearly seriesparallel.
Braess's Paradox and PowerLaw Nonlinearities in Networks
 Journal of the Australian Mathematical Society, Series B
, 1991
"... We study flows in physical networks with a potential function defined over the nodes and a flow defined over the arcs. The networks have the further property that the flow on any arc a is a given increasing function of the difference in potential between its initial and terminal node. An example is ..."
Abstract

Cited by 11 (5 self)
 Add to MetaCart
We study flows in physical networks with a potential function defined over the nodes and a flow defined over the arcs. The networks have the further property that the flow on any arc a is a given increasing function of the difference in potential between its initial and terminal node. An example is the equilibrium flow in watersupply pipe networks where the potential is the head and the HazenWilliams' rule gives the flow as a numerical factor k a times the head difference to a power, s ? 0 (and s 0:54). In the pipenetwork problem with HazenWilliams' nonlinearities, that is the same s ? 0 on each arc, given the consumptions and supplies, the power usage is a decreasing function of the conductivity factors k a . There is also a converse to this. Approximately stated it is: if the relationship between the flow and the head difference are not all power laws, with the same s on each arc, given at least 6 pipes, one can arrange (lengths of) them so that Braess's paradox occurs, i.e. on...
The graph programming language GP
 In Proc. Algebraic Informatics (CAI 2009
, 2009
"... Abstract. GP (for Graph Programs) is a rulebased, nondeterministic programming language for solving graph problems at a high level of abstraction, freeing programmers from handling lowlevel data structures. The core of GP consists of four constructs: singlestep application of a set of conditional ..."
Abstract

Cited by 11 (9 self)
 Add to MetaCart
Abstract. GP (for Graph Programs) is a rulebased, nondeterministic programming language for solving graph problems at a high level of abstraction, freeing programmers from handling lowlevel data structures. The core of GP consists of four constructs: singlestep application of a set of conditional graphtransformation rules, sequential composition, branching and iteration. This paper gives an overview on the GP project. We introduce the language by discussing a sequence of small programming case studies, formally explain conditional rule schemata which are the building blocks of programs, and present a semantics for GP in the style of structural operational semantics. A special feature of the semantics is how it uses the notion of finitely failing programs to define powerful branching and iteration commands. We also describe GP’s prototype implementation. 1
List EdgeColorings Of SeriesParallel Graphs
 ELECTRONIC JOURNAL OF COMBINATORICS
, 1999
"... It is proved that for every integer k 3, for every (simple) ..."
Abstract

Cited by 9 (1 self)
 Add to MetaCart
It is proved that for every integer k 3, for every (simple)