Approximation Algorithms for the Bottleneck Asymmetric Traveling Salesman Problem

We present the first nontrivial approximation algorithm for the bottleneck asymmetric traveling salesman problem . Given an asymmetric metric cost between n vertices, the problem is to find a Hamiltonian cycle that minimizes its bottleneck (or maximum-length edge) cost. We achieve an O (log n / log log n ) approximation performance guarantee by giving a novel algorithmic technique to shortcut Eulerian circuits while bounding the lengths of the shortcuts needed. This allows us to build on a related result of Asadpour, Goemans, Mądry, Oveis Gharan, and Saberi to obtain this guarantee. Furthermore, we show how our technique yields stronger approximation bounds in some cases, such as the bounded orientable genus case studied by Oveis Gharan and Saberi. We also explore the possibility of further improvement upon our main result through a comparison to the symmetric counterpart of the problem.

Use Of ACS 712ELC-5A Current Sensor on Overloaded Load Installation Safety System

People want energy to satisfy their each day needs. However, maximum of those energy customers are now no longer aware that using an electric powered load is too large, which regularly reasons disturbances. In coping with overload disturbances withinside the family sector, MCB is used as a protection tool. The running precept of the MCB continues to be the usage of magnetic, so it's far less effective. When disconnecting the cutting-edge because of overload, the MCB will experience a touch overdue, which could reason sparks and a hearthplace withinside the family. Therefore, on this look at a cutting-edge sensor protection circuit is designed to update the MCB. This circuit can show the cutting-edge cost at the LCD and restriction the overcurrent to a restriction of three amperes. The overload safety machine constructed from the ACS712ELC-5A cutting-edge sensor can come across currents among 0A and 5A. So, to reduce off the cutting-edge, a 12V relay is used. When trying out a ready-made machine, this protection tool can study currents withinside the variety 0A to 3A, with median studying mistakes of 0.65%. If the burden is better than 3A, the machine also can reduce the cutting-edge.

The minimum perfect matching in pseudo-dimension 0 < q < 1

It is known that for K n,n equipped with i.i.d. exp (1) edge costs, the minimum total cost of a perfect matching converges to $\zeta(2)=\pi^2/6$ in probability. Similar convergence has been established for all edge cost distributions of pseudo-dimension $q \geq 1$ . In this paper we extend those results to all real positive q, confirming the Mézard–Parisi conjecture in the last remaining applicable case.

Risk-aware graph search with dynamic edge cost discovery

In this paper, we introduce a novel algorithm for incorporating uncertainty into lookahead planning. Our algorithm searches through connected graphs with uncertain edge costs represented by known probability distributions. As a robot moves through the graph, the true edge costs of adjacent edges are revealed to the planner prior to traversal. This locally revealed information allows the planner to improve performance by predicting the benefit of edge costs revealed in the future and updating the plan accordingly in an online manner. Our proposed algorithm, risk-aware graph search (RAGS), selects paths with high probability of yielding low costs based on the probability distributions of individual edge traversal costs. We analyze RAGS for its correctness and computational complexity and provide a bounding strategy to reduce its complexity. We then present results in an example search domain and report improved performance compared with traditional heuristic search techniques. Lastly, we implement the algorithm in both simulated missions and field trials using satellite imagery to demonstrate the benefits of risk-aware planning through uncertain terrain for low-flying unmanned aerial vehicles.

Efficient Optimal Search under Expensive Edge Cost Computation

Optimal heuristic search has been successful in many domains, including journey planning, route planning and puzzle solving. Existing work typically assumes that the cost of each action can easily be obtained. However, in many problems, the exact edge cost is expensive to compute. Existing search algorithms face a significant performance bottleneck, due to an excessive overhead associated with dynamically calculating exact edge costs. We present DEA*, an algorithm for problems with expensive edge cost computations. DEA* combines heuristic edge cost evaluations with delayed node expansions, reducing the number of exact edge computations. We formally prove that DEA* is optimal and it is efficient with respect to the number of exact edge cost computations. We empirically evaluate DEA* on multiple-worker routing problems where the exact edge cost is calculated by invoking an external multi-modal journey planning engine. The results demonstrate the effectiveness of our ideas in reducing the computational time and improving the solving ability. In addition, we show the advantages of DEA* in domain-independent planning, where we simulate that accurate edge costs are expensive to compute.

Inverse min-max spanning r-arborescence problem under the weighted sum-type Hamming distance

The inverse min-max spanning [Formula: see text]-arborescence problem under the weighted sum-type Hamming distance on graphs is to modify the edge cost vector with respect to given modification bounds such that a given spanning [Formula: see text]-arborescence becomes a min-max spanning [Formula: see text]-arborescence and the total modification cost under the sum-type Hamming distance for all edges is minimized. It is shown that the problem is solvable in strongly polynomial time.