in the maximum flow network interdiction problem, an attacker attempts to minimize the maximum flow by interdicting flow on the arcs of network. in this paper, our focus is on the nodal interdiction for network instead of the arc interdiction. two path inequalities for the node-only interdiction problem are represented. it has been proved that the integrality gap of relaxation of the maximum fl...

In the maximum flow network interdiction problem, an attacker attempts to minimize the maximum flow by interdicting flow on the arcs of network. In this paper, our focus is on the nodal interdiction for network instead of the arc interdiction. Two path inequalities for the node-only interdiction problem are represented. It has been proved that the integrality gap of relaxation of the maximum fl...

In this paper a new method is introduced for path planning of an autonomous vehicle. In this method, the environment is considered cluttered and with some uncertainty sources. Thus, the state of detected object should be estimated using an optimal filter. To do so, the state distribution is assumed Gaussian. Thus the state vector is estimated by a Kalman filter at each time step. The estimation...

Capacitated fixed-charge network flows are used to model a variety of problems in telecommunication, facility location, production planning and supply chain management. In this paper, we investigate capacitated path substructures and derive strong and easy-to-compute path cover and path pack inequalities. These inequalities are based on an explicit characterization of the submodular inequalitie...

In this paper our primary concern is with the establishment of weighted Hardy inequalities in L(Ω) and Rellich inequalities in L(Ω) depending upon the distance to the boundary of domains Ω ⊂ R with a finite diameter D(Ω). Improved constants are presented in most cases.

Given a directed graph D = (N, A) and a sequence of positive integers 1 ≤ c1 < c2 < · · · < cm ≤ |N |, we consider those path and cycle polytopes that are defined as the convex hulls of simple paths and cycles of D of cardinality cp for some p ∈ {1, . . . , m}, respectively. We present integer characterizations of these polytopes by facet defining linear inequalities for which the separation pr...

We give a partial description of the (s, t)− p-path polytope of a directed graph D which is the convex hull of the incidence vectors of simple directed (s, t)-paths in D of length p. First, we point out how the (s, t) − p-path polytope is located in the family of path and cycle polyhedra. Next, we give some classes of valid inequalities which are very similar to inequalities which are valid for...

In this paper, we study some functional inequalities (such as Poincaré inequalities, logarithmic Sobolev inequalities, generalized Cheeger isoperimetric inequalities, transportation-information inequalities and transportation-entropy inequalities) for reversible nearest-neighbor Markov processes on a connected finite graph by means of (random) path method. We provide estimates of the involved c...

The fixed-charge transportation problem is a fixed-charge network flow problem on a bipartite graph. This problem appears as a subproblem in many hard transportation problems, and is also both a special case and a strong relaxation of the challenging bigbucket multi-item lot-sizing problem. In this paper, we provide a polyhedral analysis of the polynomially solvable special case in which the as...

The Traveling Deliveryman Problem is a generalization of the Minimum Cost Hamiltonian Path Problem where the starting vertex of the path, i.e. a depot vertex, is fixed in advance and the cost associated with a Hamiltonian path equals the sum of the costs for the layers of paths (along the Hamiltonian path) going from the depot vertex to each of the remaining vertices. In this paper, we propose ...