Considered is the set-up of availability of n coins and the possibility of at the most one of these coins being counterfiet in the sense of possessing slightly more or slightly less weight than that of the rest, though all the coins have remarkably identical appearance ! There has been considerable interest in the underlying combinatorial problem of checking the existence of such a coin and ide...

We study a traveling salesman problem where the path is optimized with a cost function that includes its length L as well as a certain measure C of its distance from the geometrical center of the graph. Using simulated annealing (SA) we show that such a problem has a transition point that separates two phases differing in the scaling behavior of L and C, in efficiency of SA, and in the shape of...

We describe an artificial ant colony capable of solving the travelling salesman problem (TSP). Ants of the artificial colony are able to generate successively shorter feasible tours by using information accumulated in the form of a pheromone trail deposited on the edges of the TSP graph. Computer simulations demonstrate that the artificial ant colony is capable of generating good solutions to b...

The Generalized Travelling Salesman Problem, denoted by GTSP, is a variant of the classical travelling salesman problem (TSP), in which the nodes of an undirected graph are partitioned into node sets (clusters) and the salesman has to visit exactly one node from every cluster. In this paper we described six distinct formulations of the GTSP as an integer programming. Apart from the standard for...

We provide an elementary proof of a formula for the number of northeast lattice paths that lie in a certain region of the plane. Equivalently, this formula counts the lattice points inside the Pitman–Stanley polytope of an n-tuple. Suppose that on election day a TV news network of questionable morality wants to increase their viewership as polling results come in. While the reporters cannot con...

We provide a uniform estimate for the L-norm (over any interval of bounded length) of the logarithmic derivatives of global normalizing factors associated to intertwining operators for the following reductive groups over number fields: inner forms of GL(n); quasi-split classical groups and their similitude groups; the exceptional group G2. This estimate is a key ingredient in the analysis of th...

Let tsp(G) denote the length of a shortest travelling salesman tour in a graph G. We prove that for any ε > 0, there exists a simple 2-connected planar cubic graph G1 such that tsp(G1) ≥ (1.25 − ε) · |V (G1)|, a simple 2-connected bipartite cubic graph G2 such that tsp(G2) ≥ (1.2 − ε) · |V (G2)|, and a simple 3-connected cubic graph G3 such that tsp(G3) ≥ (1.125− ε) · |V (G3)|.

In this paper we present a new Ants System approach to a dynamic Travelling Salesman Problem. Here the travel times between the cities are subject to change. To handle this dynamism several ways of adapting the pheromone matrix both locally and globally are considered. We show that the strategy of smoothing pheromone values only in the area containing a change leads to improved results.

Human visual/spatial problem solving often requires both global and local information to be processed. But the relationship between those two kinds of information and the way in which they interact with one another during problem solving has not been thoroughly discussed. In the particular setting of solving the traveling salesman problem (TSP), we investigated into the relative roles of global...