In this paper, we study dynamic shortest path problems that determine a shortest path from a specified source node to every other node in the network where arc travel times change dynamically. We consider two problems: the minimum time walk problem and the minimum cost walk problem. The minimum time walk problem is to find a walk with the minimum travel time. The minimum cost walk problem is to...

In this paper, we study inverse optimization problems defined as follows: Let S denote the set of feasible solutions of an optimization problem P, let c be a specified cost vector, and x0 be a given feasible solution. The solution x0 may or may not be an optimal solution of P with respect to the cost vector c. The inverse optimization problem is to perturb the cost vector c to d so that x0 is a...

Let G = (V, E) be a connected multigraph, whose edges are associated with labels specified by an integer-valued function L : E → N. In addition, each label ` ∈ N has a non-negative cost c(`). The minimum label spanning tree problem (MinLST) asks to find a spanning tree in G that minimizes the overall cost of the labels used by its edges. Equivalently, we aim at finding a minimum cost subset of ...

Ford and Fulkerson’s original 1956 max flow/min cut paper formulated max flow in terms of flows on paths, rather than the more familiar flows on arcs. In 1974 Hoffman pointed out that Ford and Fulkerson’s original proof was quite abstract, and applied to a wide range of flow problems. In this abstract model we have capacitated elements, and linearly ordered subsets of elements called paths. Whe...

In this paper we formulate and study an optimal path problem on networks that extends the minimum cost path problem in the weighted directed graphs. Let G = (X,E) be a finite directed graph with vertex set X, |X| = n and edge set E where to each directed edge e = (u, v) ∈ E a cost ce is associated. Assume that for two given vertices x, y there exists a directed path P (x, y) = {x = x0, e0, x1, ...

We investigate how to solve several classical network flow problems using secure multi-party computation. We consider the shortest path problem, the minimum mean cycle problem and the minimum cost flow problem. To the best of our knowledge, this is the first time the two last problems have been addressed in a general multi-party computation setting. Furthermore, our study highlights the complex...

This paper considers the problem of designing fast, approximate, combinatorial algorithms for multicommodity flows and other fractional packing problems. We provide a different approach to these problems which yields faster and much simpler algorithms. Our approach also allows us to substitute shortest path computations for min-cost flow computations in computing maximum concurrent flow and min...

The typical objective of path planning is to find the shortest feasible path. Many times, however, there may be no solution given the existence of constraints, such as obstacles. In these cases, the minimum constraint removal problem asks for the minimum set of constraints that need to be removed from the state space to find a solution. Unfortunately, minimum constraint removal paths do not exh...

We study the task of computing a matching between two images by formulating it as an instance of the minimum-cost flow problem. Here, we use a cycle cancelling algorithm to find the optimal flow. To reduce the practical runtime, we propose a hierarchical scheme in which the images are first scaled down and then the optimal solution for the smaller problem is used as a starting point for the hig...

The problem to find a valid integer flow with flow multipliers on nodes or arcs is long known to be NP-complete [10]. We show that the problem is still hard when restricted to instances with a limited number of integral multipliers. To find an integer minimum cost maximal pseudoflow, respecting only the node balance constraints of the inner nodes, is also still a difficult task. Further, we dem...