Journal ArticleDOI
Negative-cycle detection algorithms
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TLDR
One of out discoveries is that a cycle detection strategy of Tarjan greatly improves computational performance of a classical shortest path algorithm, making it competitive with the fastest known algorithms on a wide range of problems.Abstract:
We study the problem of finding a negative length cycle in a network. An algorithm for the negative cycle problem combines a shortest path algorithm and a cycle detection strategy. We survey cycle detection strategies, study various combinations of shortest path algorithms and cycle detection strategies and find the best combinations. One of out discoveries is that a cycle detection strategy of Tarjan greatly improves computational performance of a classical shortest path algorithm, making it competitive with the fastest known algorithms on a wide range of problems. As a part of out study, we develop problem families for testing negative cycle algorithms.read more
Citations
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Book ChapterDOI
Satisfiability Modulo Theories
Clark Barrett,Cesare Tinelli +1 more
TL;DR: The architecture of a lazy SMT solver is discussed, examples of theory solvers are given, how to combine such solvers modularly is shown, and several extensions of the lazy approach are mentioned.
Journal ArticleDOI
Lazy Satisfiability Modulo Theories
TL;DR: An extensive survey of SMT, with particular focus on the lazy approach, survey, classify and analyze from a theory-independent perspective the most effective techniques and optimizations which are of interest for lazy SMT and which have been proposed in various communities.
Book ChapterDOI
Think Locally, Act Globally: Highly Balanced Graph Partitioning
Peter Sanders,Christian Schulz +1 more
TL;DR: A novel local improvement scheme for graph partitions that allows to enforce strict balance constraints and is able to improve or reproduce many of the best known perfectly balanced partitioning results reported in the Walshaw benchmark.
Journal ArticleDOI
Experimental analysis of the fastest optimum cycle ratio and mean algorithms
TL;DR: This article focuses on the fastest OCR algorithms only, provides a unified theoretical framework and a few new results, and runs these algorithms on the largest circuit benchmarks available.
Book ChapterDOI
A SAT Based Approach for Solving Formulas over Boolean and Linear Mathematical Propositions
TL;DR: In this paper, a general and efficient approach to the problem is presented, based on two main ingredients: a DPLL-based SAT procedure for dealing efficiently with the propositional component of the problem, and a tight integration, within the DPLL architecture, of a set of mathematical deciders for theories of increasing expressive power.
References
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Journal ArticleDOI
A note on two problems in connexion with graphs
TL;DR: A tree is a graph with one and only one path between every two nodes, where at least one path exists between any two nodes and the length of each branch is given.
Book
Introduction to Algorithms
TL;DR: The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures and presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers.
Book
Flows in networks
D. R. Ford,D. R. Fulkerson +1 more
TL;DR: Ford and Fulkerson as mentioned in this paper set the foundation for the study of network flow problems and developed powerful computational tools for solving and analyzing network flow models, and also furthered the understanding of linear programming.
Journal ArticleDOI
On a routing problem
TL;DR: Given a set of N cities, with every two linked by a road, and the times required to traverse these roads, the functional equation technique of dynamic programming and approximation in policy space yield an iterative algorithm which converges after at most (N-1) iterations.