Stochastic shortest path (SSP) problems arise in a variety of discrete stochastic control contexts. An optimal solution to such a problem is typically computed using the value function, which can be found by solving the corresponding dynamic programming equations. In the deterministic case, these equations can be often solved by the highly efficient label-setting methods (such as Dijkstra’s and...

Abstract In this paper we prove the equivalence between some known notions of solutions to eikonal equation and more general analogs Hamilton-Jacobi equations in complete rectifiably connected metric spaces. The considered are that curve-based viscosity solutions, slope-based Monge solutions. By using induced intrinsic (path) metric, reduce space a length show these associated Dirichlet boundar...

Stochastic shortest path (SSP) problems arise in a variety of discrete stochastic control contexts. An optimal solution to such a problem is typically computed using the value function, which can be found by solving the corresponding dynamic programming equations. In the deterministic case, these equations can be often solved by highly efficient label-setting methods (such as Dijkstra’s and Dia...

In this paper we analyze a Boltzmann type mean field game model for knowledge growth, which was proposed by Lucas and Moll [14]. We discuss the underlying mathematical model, which consists of a coupled system of a Boltzmann type equation for the agent density and a Hamilton-Jacobi-Bellman equation for the optimal strategy. We study the analytic features of each equation separately and show loc...

Recently, wormhole routers with multi-destination capability have been proposed to support fast multicast in a multi-computer network. To avoid communication deadlock, existing results have proposed to construct a Hamilton path, Euler path, trip, or their variants, in the network, perhaps with some degree of support of virtual channels 1, 14, 15, 18, 23]. In this paper, we identify that a netwo...

It is shown that for any set of 2n points in general position in the plane there is a non-crossing perfect matching of n straight line segments whose total length is at least 2/π of the maximum possible total length of a (possibly crossing) perfect matching on these points. The constant 2/π is best possible and a non-crossing matching whose length is at least as above can be found in polynomial...

Suppose a graph G = (V, E) with edge weights w(e) and edges partitioned into disjoint categories S1, . . . , Sp is given. We consider optimization problems P on G defined by a family of feasible sets D(G) and the following objective function: L5(D) = max 1≤i≤p ( max e∈Si∩D w(e)− min e∈Si∩D w(e) ) For an arbitrary number of categories we show that the L5-perfect matching, L5-a-b path, L5-spannin...

Let G be a directed graph and H a subgraph of G. A D(G,H, λ) design is a multiset D of subgraphs of G each isomorphic to H so that every directed 2-path in G lies in exactly λ subgraphs in D. In this paper, we show that there exists a D(K∗ n,n, −→ C 2n, 1) design for every n ≥ 2, where K∗ n,n is the complete bipartite directed graph and −→ C 2n is a directed Hamilton cycle in K∗ n,n.

An intriguing open question is whether the graph formed by the middle two levels of the Boolean lattice of subsets of a k element set has a Hamilton path for all k We consider nding a lower bound on the length of the longest cycle in this graph A result of Babai for vertex transitive graphs gives a lower bound of N where N is the total number of vertices in the middle two levels In this paper w...

Simple cosmological models are used to show that gravitation can be quantized as an ordinary gauge system if the Hamilton-Jacobi equation for the model under consideration is separable. In this situation, a canonical transformation can be performed such that in terms of the new variables the model has a linear and homogeneous constraint, and therefore canonical gauges are admissible in the path...