Cycle detection

Abstract: As graph data is prevalent for an increasing number of Internet applications, continuously monitoring structural patterns in dynamic graphs in order to generate real-time alerts and trigger prompt actions becomes critical for many applications In this paper, we present a new system GraphS to efficiently detect constrained cycles in a dynamic graph, which is changing constantly, and return the satisfying cycles in real-time A hot point based index is built and efficiently maintained for each query so as to greatly speed-up query time and achieve high system throughput The GraphS system is developed at Alibaba to actively monitor various online fraudulent activities based on cycle detection For a dynamic graph with hundreds of millions of edges and vertices, the system is capable to cope with a peak rate of tens of thousands of edge updates per second and find all the cycles with predefined constraints with a 999% latency of 20 milliseconds

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 study various combinations of shortest path algorithms and cycle detection strategies and find the best combinations. One of our discoveries is that a cycle detection strategy of Tarjan greatly improves practical 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 our study, we develop problem families for testing negative cycle algorithms.

Abstract: In this note, we propose a matrix-based approach for asynchronous sequential machines. Using semi-tensor product of matrices, we convert an asynchronous machine into a discrete-time bilinear system, and study its dynamics by investigating its structure matrices. We give simple algorithms for cycle detection and reachability analysis, and moreover, provide a control design method for the model matching of two input/state machines.

Abstract: Fair-cycle detection, a core problem in model checking, is solvable in linear time in the size of the design model using an explicit-state representation. Existing cycle-detection algorithms for symbolic model checking are quadratic or n log n time in the worst case and often inefficient in practice. Which default symbolic cycle-detection algorithm to implement in model checkers remains an open question. We compare several such algorithms based on the numbers of external and internal iterations and the numbers of image operations that they perform on both randomly-generated and real examples. Unlike recent work by Ravi, Bloem, and Somenzi, we conclude that model checkers need to implement at least two generic cycle-detection algorithms: the traditional Emerson-Lei algorithm and one that evolved from our study, originally due to Hojati et al. We demonstrate that these two algorithms are complementary, as the latter algorithm is provably incomparable to Emerson-Lei's and often dominates it in practice.