We study atomic routing games on networks in which players choose a path with the objective of minimizing the maximum congestion along the edges of their path. The social cost is the global maximum congestion over all edges in the network. We show that the price of stability is 1. The price of anarchy, PoA, is determined by topological properties of the network. In particular, PoA = O(`+ log n)...

This thesis presents an optimal algorithm that solves the longest path problem for undirected graphs. The algorithm makes use of graph partitioning and dynamic programming. It’s performance was evaluated in a number of benchmarks and compared to other known algorithms. The runtime of the algorithm was shown to be significantly faster on the tested graphs. Deutsche Zusammenfassung Diese Arbeit p...

New algorithm for finding longest increasing subsequence is discussed. This algorithm is based on the ideas of idempotent mathematic and uses Max-Plus idempotent semiring. Problem of finding longest increasing subsequence is reformulated in a matrix form and solved with linear algebra.

Wavelength-routed WDM optical network has the tremendous capability of providing overgrowing needs of higher bandwidth to the end users. It uses preconfigured optimal lightpaths to carry the traffic of users from one node to another node. Hence, an intelligent RWA algorithms required to be employed to achieve better performance of the network. In this paper, we investigate the impact of path le...

S of the Ghent Graph Theory Workshop on Longest Paths and Longest Cycles Kathie Cameron Degree-constrained spanning trees 2 Jan Goedgebeur Finding minimal obstructions to graph coloring 3 Jochen Harant On longest cycles in essentially 4-connected planar graphs 3 Frantǐsek Kardoš Barnette was right: not only fullerene graphs are Hamiltonian 4 Gyula Y. Katona Complexity questions for minimally t-...

We present the first streaming algorithm for the longest path problem in undirected graphs. The input graph is given as a stream of edges and RAM is limited to only a linear number of edges at a time (linear in the number of vertices n). We prove a per-edge processing time of O(n), where a naive solution would have required Ω(n2). Moreover, we give a concrete linear upper bound on the number of...

It has been recognized that the existing routing architecture of today’s Internet is facing scalability problems. Although deployment of CIDR (Classless Inter-Domain Routing) slows the growth of global routing tables, LPM (longest prefix matching), which is greedily pursuing for more-specific prefixes, seriously restricts the advance of scalable routing. The prevalent LPM algorithm for routing ...

We present a method to find static path exclusions in a control flow graph in order to refine the WCET analysis. Using this information, some infeasible paths can be discarded during the ILP-based longest path analysis which helps to improve precision. The new analysis works at the assembly level and uses the Omega library to evaluate Presburger formulas.

In this paper, we develop an acyclic network of queues for the design of a dynamic flow shop, where each service station represents a machine. The orders arrive at the input station according to a Poisson process, assuming each order consists of n jobs. Jobs associated with successive orders contend for resources on a FCFS (First Come First Served) dispatching rule in all machines. Upon arrivin...

We consider the minimum-weight path between any pair of nodes of the n-vertex complete graph in which the weights of the edges are i.i.d. exponentially distributed random variables. We show that the longest of these minimum-weight paths has about α logn edges where α ≈ 3.5911 is the unique solution of the equation α logα − α = 1. This answers a question left open by Janson [8].