Yannis Manoussakis

Scheduling Independent Multiprocessor Tasks

We study the problem of scheduling a set of n independent multiprocessor tasks with prespecified processor allocations on a fixed number of processors. We propose a linear time algorithm that finds a schedule of minimum makespan in the preemptive model, and a linear time approximation algorithm that finds a schedule of length within a factor of (1 + c) of optimal in the non-preemptive model.

CYCLES AND PATHS IN BIPARTITE TOURNAMENTS WITH SPANNING CONFIGURATIONS

We give necessary and sufficient conditions in terms of connectivity and factors for the existence of hamiltonian cycles and hamiltonian paths and also give sufficient conditions in terms of connectivity for the existence of cycles through any two vertices in bipartite tournaments.

Paths and trails in edge-colored graphs

This paper deals with the existence and search for properly edge-colored paths/trails between two, not necessarily distinct, vertices s and t in an edge-colored graph from an algorithmic perspective. First we show that several versions of the s-t path/trail problem have polynomial solutions including the shortest path/trail case. We give polynomial algorithms for finding a longest properly edge-colored path/trail between s and t for a particular class of graphs and characterize edge-colored graphs without properly edge-colored closed trails. Next, we prove that deciding whether there exist k pairwise vertex/edge disjoint properly edge-colored s-t paths/trails in a c-edge-colored graph G^c is NP-complete even for k=2 and c=@W(n^2), where n denotes the number of vertices in G^c. Moreover, we prove that these problems remain NP-complete for c-edge-colored graphs containing no properly edge-colored cycles and c=@W(n). We obtain some approximation results for those maximization problems together with polynomial results for some particular classes of edge-colored graphs.

Minimal colorings for properly colored subgraphs

We give conditions on the minimum numberk of colors, sufficient for the existence of given types of properly edge-colored subgraphs in ak-edge-colored complete graph. The types of subgraphs we study include families of internally pairwise vertex-disjoint paths with common endpoints, hamiltonian paths and hamiltonian cycles, cycles with a given lower bound of their length, spanning trees, stars, and cliques. Throughout the paper, related conjectures are proposed.

Cycles and paths of many lengths in bipartite digraphs

Abstract We give several sufficient conditions on the half-degrees of a bipartite digraph for the existence of cycles and paths of various lengths. Some analogous results are obtained for bipartite oriented graphs and for bipartite tournaments.

The forwarding index of directed networks

Abstract In a given network with n vertices, a routing is defined as a set of n(n — 1) paths, one path connecting each ordered pair of vertices. The load of a vertex is the number of paths going through it. The forwarding index of the network is the minimum of the largest load taken over all routings. We give upper bounds on the forwarding index in k-connected digraphs and in digraphs with half-degrees at least k. Related conjectures are proposed.

Directed Hamiltonian graphs

We give a new condition involving degrees sufficient for a digraph to be hamiltonian.

Polynomial algorithms for finding cycles and paths in bipartite tournaments

Efficient algorithms for finding Hamiltonian cycles, Hamiltonian paths, and cycles through two given vertices in bipartite tournaments are given.

A polynomial algorithm for Hamiltonian-connectedness in semicomplete digraphs

Abstract We describe a polynomial algorithm, which either finds a Hamiltonian path with prescribed initial and terminal vertices in a tournament (in fact, in any semicomplete digraph), or decides that no such path exists.

Minimum (2, r )-metrics and integer multiflows

Abstract LetH=(T, U)be a connected graph. AT-partitionof a setV⊇Tis a partition ofVinto subsets, each containing exactly one element ofT. We start with the following problem (*): given a multigraphG=(V, E)withV⊇T,find aT-partition Π ofVthat minimizes the sum of productsd(s, t)n(s, t)over alls,t∈T.Hered(s, t)is the distance fromstotinHandn(s, t)is the number of edges ofGbetween the sets in Π that containsandt.When the graphHis complete, (*) turns into the minimum multiway cut problem, which is known to be NP-hard even if|T|=3.On the other hand, whenHis the complete bipartite graphK2,rwith parts of 2 andr=|T|−2nodes, (*) is specialized to be the minimum (2,r)-metric problem, which can be solved in polynomial time. We prove that the multicommodity flow problem dual of the minimum (2,r)-metric problem has an integer optimal solution wheneverGisinner Eulerian(i.e. the degree of each node inV−Tis even), and such a solution can be found in polynomial time. Another nice property ofK2,ris that, independently ofG,the optimum objective value in (*) is the same as that in its factional relaxation. We call a graphHwith a similar propertyminimizableand give a description of the minimizable graphs in polyhedral terms. Finally, we show that every tree is minimizazble.