Negative-cycle detection algorithms

Cherkassky, Boris V.; Goldberg, Andrew V.

doi:10.1007/3-540-61680-2_67

Cited by 68 publications

(88 citation statements)

References 15 publications

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“…The weight of the inserted edges is set to zero. We can apply a standard shortest path algorithm [39] that can handle negative edge weights to detect a negative cycle. If the model contains a negative cycle, we can perform a set of node movements that will not alter the balance of the blocks since each block obtains and emits a node.…”

Section: Basic Idea -Using a Negative Cycle Detection Algorithmmentioning

confidence: 99%

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High quality graph partitioning

Sanders¹,

Schulz²

2013

Contemporary Mathematics

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Section: Basic Idea -Using a Negative Cycle Detection Algorithmmentioning

confidence: 99%

“…We have implemented the algorithms described within this chapter using C++. We implemented negative cycle detection with subtree disassembly and distance updates as described in [39]. The implementation of the balanced local search algorithms has about 3 400 lines of code.…”

Section: Experimental Evaluationmentioning

confidence: 99%

High quality graph partitioning

Sanders¹,

Schulz²

2013

Contemporary Mathematics

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“…1 is an adaptation of Tarjan's subtree disassembly method for negative cycle detection in static graphs [1]. We henceforth refer to this modified algorithm as the "Adaptive Bellman-Ford algorithm" or ABF algorithm, to stress that it adapts a solution to the original graph to obtain the solution to the constraints corresponding to the altered graph.…”

Section: The Adaptive Bellman-ford Algorithmmentioning

confidence: 99%

“…Several problems in circuits and systems theory require the solving of constraint equations [1,2,3]. Examples include VLSI layout compaction, computing maximum operational speed of circuits, and performance analysis of interactive (reactive) systems.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive negative cycle detection in dynamic graphs

Chandrachoodan

Bhattacharyya

Liu

2001

ISCAS 2001. The 2001 IEEE International Symposium on Circuits and Systems (Cat. No.01CH37196)

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We examine the problem of detecting negative cycles in a dynamic graph, which is a fundamental problem that arises in electronic design automation and systems theory.We introduce the concept of adaptive negative cycle detection, in which a graph changes over time, and negative cycle detection needs to be done periodically, but not necessarily after every individual change. Such scenarios arise, for example, during iterative design space exploration for hardware and software synthesis. We present an algorithm for this problem, called the Adaptive Bellman-Ford (ABF) algorithm, based on a novel extension of the well known Bellman-Ford algorithm. The ABF algorithm allows us to systematically adapt information for a given graph to a modified version of the graph. We show that the ABF algorithm significantly outperforms previously available approaches for dynamic graphs, which either recompute negative cycle information from scratch whenever a graph is modified, or process the modifications one at a time ("incrementally").As an application of the ABF technique, we show that it can be used to obtain a very fast implementation of Lawler's technique for the computation of the maximum-cycle mean (MCM) of a graph, especially for a certain important kind of sparse graph. We further illustrate the application of the ABF technique to design-space exploration by developing automated search techniques for scheduling iterative data-flow graphs.

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Models and heuristics for a minimum arborescence problem

et al. 2007

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The Minimum Arborescence problem (MAP) consists of finding a minimum cost arborescence in a directed graph. This problem is NP-Hard and is a generalization of two well-known problems: the Minimum Spanning Arborescence Problem (MSAP) and the Directed Node Weighted Steiner Tree Problem (DNWSTP). We start the model presentation in this paper by describing four models for the MSAP (including two new ones, using so called "connectivity" constraints which forbid disconnected components) and we then describe the changes induced on the polyhedral structure of the problem by the removal of the spanning property. Only two (the two new ones) of the four models for the MSAP remain valid when the spanning property is removed. We also describe a multicommodity flow reformulation for the MAP that differs from well-known multicommodity flow reformulations in the sense that the flow conservation constraints at source and destination are replaced by inequalities. We show that the linear programming relaxation of this formulation is equivalent to the linear programming relaxation of the best of the two previous valid formulations and we also propose two Lagrangean relaxations based on the multicommodity flow reformulation. From the upper bound perspective, we describe a constructive heuristic as well as a local search procedure involving the concept of key path developed earlier for the Steiner Tree Problem. Numerical experiments taken from instances with up

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Negative-cycle detection algorithms

Cited by 68 publications

References 15 publications

High quality graph partitioning

High quality graph partitioning

Adaptive negative cycle detection in dynamic graphs

Models and heuristics for a minimum arborescence problem

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