A Zero-Space algorithm for Negative Cost Cycle Detection in networks

AbstractThis paper is concerned with the problem of checking whether a network with positive and negative costs on its arcs contains a negative cost cycle. The Negative Cost Cycle Detection (NCCD) problem is one of the more fundamental problems in network design and finds applications in a number of domains ranging from Network Optimization and Operations Research to Constraint Programming and System Verification. As per the literature, approaches to this problem have been either Relaxation-based or Contraction-based. We introduce a fundamentally new approach for negative cost cycle detection; our approach, which we term as the Stressing Algorithm, is based on exploiting the connections between the NCCD problem and the problem of checking whether a system of difference constraints is feasible. The Stressing Algorithm is an incremental, comparison-based procedure which is as efficient as the fastest known comparison-based algorithm for this problem. In particular, on a network with n vertices and m edges, the Stressing Algorithm takes O(m⋅n) time to detect the presence of a negative cost cycle or to report that none exists. A very important feature of the Stressing Algorithm is that it uses zero extra space; this is in marked contrast to all known algorithms that require Ω(n) extra space. It is well known that the NCCD problem is closely related to the Single Source Shortest Paths (SSSP) problem, i.e., the problem of determining the shortest path distances of all the vertices in a network, from a specified source; indeed most algorithms in the literature for the NCCD problem are modifications of approaches to the SSSP problem. At this juncture, it is not clear whether the Stressing Algorithm could be extended to solve the SSSP problem, even if O(n) extra space is available

Restoring efficiency, removing sound

Increased renewable power generation, HVDC interconnections and geomagnetic effects all bias the AC grid with small direct currents which leads to two negative effects on transformers (theory of half-cycle saturation) increased noise and increased no-load losses. A unique solution is the DC compensation system, which is an add-on to a transformer which eliminates the DC effects. Furthermore, there are dedicated steps available, from pure detection of the problem, preparation of the transformer and measurement, all the way up to a full compensation system

Improved Algorithms for Computing the Cycle of Minimum Cost-to-Time Ratio in Directed Graphs

We study the problem of finding the cycle of minimum cost-to-time ratio in a directed graph with n nodes and m edges. This problem has a long history in combinatorial optimization and has recently seen interesting applications in the context of quantitative verification. We focus on strongly polynomial algorithms to cover the use-case where the weights are relatively large compared to the size of the graph. Our main result is an algorithm with running time ~O(m^{3/4} n^{3/2}), which gives the first improvement over Megiddo\u27s ~O(n^3) algorithm [JACM\u2783] for sparse graphs (We use the notation ~O(.) to hide factors that are polylogarithmic in n.) We further demonstrate how to obtain both an algorithm with running time n^3/2^{Omega(sqrt(log n)} on general graphs and an algorithm with running time ~O(n) on constant treewidth graphs. To obtain our main result, we develop a parallel algorithm for negative cycle detection and single-source shortest paths that might be of independent interest

Negative Cycle Detection in Dynamic Graphs

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. Previous approaches used for this have tried to modify Dijkstra's algorithm since it is the fastest known Single-Source Shortest Path algorithm. We introduce the concept of {\em batch mode} negative cycle detection, in which a graph changes over time, and negative cycle detection needs to be done periodically. Such scenarios arise, for example, during iterative design space exploration for hardware and software synthesis. We present an algorithm for this problem, based on the Bellman-Ford algorithm, which outperforms previous approaches. We also show that this technique leads to very fast algorithms for the computation of the maximum-cycle mean (MCM) of a graph, especially for a certain form of {\em sparse graph}. Such sparseness often occurs in practice, as demonstrated for example by the ISCAS 89/93 benchmarks. We present experimental results that demonstrate the advantages of our batch-processing techniques, and illustrate their application to design-space exploration by developing an automated local-search technique for multiple-voltage scheduling of iterative data-flow graphs. (Also cross-referenced as UMIACS-TR-99-59

Data-Efficient Minimax Quickest Change Detection with Composite Post-Change Distribution

The problem of quickest change detection is studied, where there is an additional constraint on the cost of observations used before the change point and where the post-change distribution is composite. Minimax formulations are proposed for this problem. It is assumed that the post-change family of distributions has a member which is least favorable in some sense. An algorithm is proposed in which on-off observation control is employed using the least favorable distribution, and a generalized likelihood ratio based approach is used for change detection. Under the additional condition that either the post-change family of distributions is finite, or both the pre- and post-change distributions belong to a one parameter exponential family, it is shown that the proposed algorithm is asymptotically optimal, uniformly for all possible post-change distributions.Comment: Submitted to IEEE Transactions on Info. Theory, Oct 2014. Preliminary version presented at ISIT 2014 at Honolulu, Hawai