st-orientations (st-numberings) or bipolar orientations of undirected graphs are central to many graph algorithms and applications. Several algorithms have been proposed in the past to compute an st-orientation of a biconnected graph. However, as indicated in [1], the computation of more than one st-orientation is very important for many applications in multiple research areas, such as this of ...

We show that the Castelnuovo–Mumford regularity of the binomial edge ideal of a graph is bounded below by the length of its longest induced path and bounded above by the number of its vertices.

Program activity graphs (PAGs) can be constructed from timestamped traces of appropriate execution events. Information about the activities on the k longest execution paths is useful in the analysis of parallel program performance. In this paper, four algorithms for finding the near–critical paths of PAGs are compared, including a best–first search (BFS) algorithm that is worst–case asymptotica...

Ant Colony Optimization (ACO) technique deals with exploratory behavior of ants while finding food by following a path based on the concentration of the pheromone. A major limitation with ACO algorithm is "stagnation". This occurs when all ants try to follow same path to reach the destination due to higher pheromone concentration and causes congestion when applied to Adhoc Wireless Ne...

We consider the likely size of the endpoint sets produced by Posa rotations, when applied to a longest path in a random graph with cn, c ≥ 2.7 edges that is conditioned to have minimum degree at least three.

We consider the likely size of the endpoint sets produced by Posa rotations, when applied to a longest path in a random graph with cn, c ≥ 2.7 edges that is conditioned to have minimum degree at least three.

In this paper, we prove that there exists a schedule for routing any set of packets with edge-simple paths, on any network, in O(c+d) steps, where c is the congestion of the paths in the network, and d is the length of the longest path. The result has applications to packet routing in parallel machines, network emulations, and job-shop scheduling.

We propose an optimal algorithm for solving the longest path problem in undirected weighted graphs. By using graph partitioning and dynamic programming, we obtain an algorithm that is significantly faster than other state-of-the-art methods. This enables us to solve instances that have previously been unsolved. 1998 ACM Subject Classification G.2.2 Graph Theory

The two-dimensional Traveling Salesperson Problem (TSP) requires finding the shortest tour through n locations. Untrained adults are adept at the task and reliably outperform simple construction algorithms for n ≤ 60. Performance may stem from a specific inherent ability. Alternatively, it may reflect general spatial intelligence, whether inherent or acquired. If the latter holds, then people s...

In this paper, we consider a nite set of generic tasks that we execute a large number of times. We introduce the linear constraints between two generic tasks : the di erence of iteration indices between the execution of two tasks subject to a precedence constraint is a linear function of these indices. These constraints are modeled by a linear graph G. Moreover, we consider no resource constrai...