George F. Georgakopoulos

Nash equilibria in all-optical networks

We consider the problem of routing a number of communication requests in WDM (wavelength division multiplexing) all-optical networks from the standpoint of game theory. If we view each routing request (pair of source-target nodes) as a player, then a strategy consists of a path from the source to the target and a frequency (color). To reflect the restriction that two requests must not use the same frequency on the same edge, conflicting strategies are assigned a prohibitively high cost. Under this formulation, we consider several natural cost functions focusing on the existence of Nash equilibria and on the complexity of recognizing and computing them.

On the Synthetic Generation of Semantic Web Schemas

In order to cope with the expected size of the Semantic Web ( SW ) in the coming years, we need to benchmark existing SW tools (e.g., query language interpreters) in a credible manner. In this paper we present the first RDFS schema generator, termed PoweRGen, which takes into account the morphological features that schemas frequently exhibit in reality. In particular, we are interested in generating synthetically the two core components of an RDFS schema, namely the property(relationships between classes or attributes) and the subsumption(subsumption relationships among classes) graph. The total-degree distribution of the former, as well as the out-degree distribution of the Transitive Closure ( TC ) of the latter, usually follow a power-law . PoweRGen produces synthetic property and subsumption graphs whose distributions respect the power-law exponents given as input with a confidence ranging between 90 ? 98%.

Max-Density Revisited: a Generalization and a More Efficient Algorithm

We present an algorithm that given a graph computes a subgraph of maximum ‘density’. (For unweighed graphs, density is the edges-to-vertices ratio). The proposed algorithm is asymptotically more efficient than the currently available ones. Our approach remains efficient for weighed graphs and more generally for weighed set-systems. Two faster approximation algorithms are offered, and a number of applications are discussed.

General Splay: A Basic Theory and Calculus

For storage and retrieval applications where access frequencies are biased, uniformly-balanced search trees may be suboptimal. Splay trees address this issue, providing a means for searching which is statically optimum and conjectured to be dynamically optimum. Subramanian explored the reasons for their success, expressing local transformations as templates and giving sufficient criteria for a template family to exhibit amortized O(log N) performance. We present a different formulation of the potential function, based on progress factors along edges. Its decomposition w.r.t. a template enables us to relax all of Subramanians conditions. Moreover it illustrates the reasons why template-based self-adjustment schemes work, and provides a straightforward way of evaluating the efficiency of such schemes.

PoweRGen: A power-law based generator of RDFS schemas

As the amount of RDF datasets available on the Web has grown significantly over the last years, scalability and performance of Semantic Web (SW) systems are gaining importance. Current RDF benchmarking efforts either consider schema-less RDF datasets or rely on fixed RDFS schemas. In this paper, we present the first RDFS schema generator, termed PoweRGen, which takes into account the features exhibited by real SW schemas. It considers the power-law functions involved in (a) the combined in- and out-degree distribution of the property graph (which captures the domains and ranges of the properties defined in a schema) and (b) the out-degree distribution of the transitive closure (TC) of the subsumption graph (which essentially captures the class hierarchy). The synthetic schemas generated by PoweRGen respect the power-law functions given as input with an accuracy ranging between 89 and 96%, as well as, various morphological characteristics regarding the subsumption hierarchy depth, structure, etc.

Precedence Constrained Scheduling: A Case in P

‘Unit execution time’ precedence constrained scheduling (UET) is an NP-complete problem with very few special cases known to be solvable in P-time. In this article we present a practically useful case of UET solvable in P-time: we show that if the task graph is given in levels that are ‘locally’ of in-degree two and of ‘width’ more than 1.55 times the number of processors (plus 1), then an optimal schedule can be found in P-time. Task graphs which represent algebraic computations fall ordinarily in this category. Our algorithm is based on a limited look-ahead technique which allows us to use it in an on-line fashion. In the appendix we give two short NP-completeness proofs which suggest that both ‘width’ and ‘degree’ restrictions are needed to get a polynomially solvable subcase.