Christos Nomikos

Routing and path multicoloring

Abstract In optical networks it is important to make an optimal use of the available bandwidth. Given a set of requests the goal is to satisfy them by using a minimum number of wavelengths. We introduce a variation to this well known problem, by allowing multiple parallel links, in order to be able to satisfy any set of requests even if the available bandwidth is insufficient. In this new approach the goal is to use a minimum number of active links and thus reduce network pricing. In graph-theoretic terms, given a graph, a list of pairs of vertices, and a number of available colors, the goal is to route paths with the given pairs of vertices as endpoints and to find a color assignment to paths that minimizes color collisions over all possible routings and colorings. We present efficient algorithms for simple network topologies. For chains our solutions are optimal; for stars and rings — where it is NP-hard to solve the problem optimally — our solutions are approximate within a factor two of the optimal solution. The key technique involves transformation to edge coloring of bipartite graphs. For rings we also present a 2-approximation algorithm, for a variation of the problem, in which the routing is already prescribed.

Routing and wavelength assignment in multifiber WDM networks with non-uniform fiber cost

Motivated by the increasing importance of multifiber WDM networks we study a routing and wavelength assignment problem in such networks. In this problem the number of wavelengths per fiber is given and the goal is to minimize the cost of fiber links that need to be reserved in order to satisfy a set of communication requests; we introduce a generalized setting where network pricing is non-uniform, that is the cost of hiring a fiber may differ from link to link. We consider two variations: undirected, which corresponds to full-duplex communication, and directed, which corresponds to one-way communication. Moreover, for rings we also study the problem in the case of pre-determined routing. We present exact or constant-ratio approximation algorithms for all the above variations in chain, ring and spider networks.

Satisfying a maximum number of pre-routed requests in all-optical rings

We address the problem of maximizing the number of satisfied requests in all-optical networks that use wavelength division multiplexing . We consider the case where requests are pre-routed and formulate it as the maximum path coloring problem. We study the problem for rings and present a (2/3)-approximation algorithm. Along the way we develop a fast matching technique for a special class of bipartite graphs. By using this technique we achieve an O( n + m log L ) time complexity for our approximation algorithm, where n is the number of nodes, m is the number of requests and L is the maximum load of requests on a single link.

Fiber Cost reduction and Wavelength minimization in multifiber WDM networks

Motivated by the increasing importance of multifiber WDM networks we study two routing and wavelength assignment problems in such networks: Fiber Cost Minimization: the number of wavelengths per fiber is given and we want to minimize the cost of fiber links that need to be reserved in order to satisfy a set of communication requests; we introduce a generalized setting where network pricing is nonuniform, that is the cost of hiring a fiber may differ from link to link. Wavelength Minimization: the number of available parallel fibers on each link is given and we want to minimize the wavelengths per fiber that are needed in order to satisfy a set of communication requests.

Notions of Bisimulation for Heyting-Valued Modal Languages

We examine the notion of bisimulation and its ramifications, in the context of the family of Heyting-valued modal languages introduced by M. Fitting. Each modal language in this family is built on an underlying space of truth values, a Heyting algebra H. All the truth values are directly represented in the language, which is interpreted on relational frames with an H-valued accessibility relation. We define two notions of bisimulation that allow us to obtain truth invariance results. We provide game semantics and, for the more interesting and complicated notion, we are able to provide characteristic formulae and prove a Hennessy–Milner-type theorem. If the underlying algebra H is finite, Heyting-valued modal models can be equivalently reformulated to a form relevant to epistemic situations with many interrelated experts. Our definitions and results draw inspiration from this formulation, which is of independent interest to Knowledge Representation applications.

Well-Founded semantics for boolean grammars

Boolean grammars [A. Okhotin, Information and Computation 194 (2004) 19-48] are a promising extension of context-free grammars that supports conjunction and negation. In this paper we give a novel semantics for boolean grammars which applies to all such grammars, independently of their syntax. The key idea of our proposal comes from the area of negation in logic programming, and in particular from the so-called well-founded semantics which is widely accepted in this area to be the “correct” approach to negation. We show that for every boolean grammar there exists a distinguished (three-valued) language which is a model of the grammar and at the same time the least fixed point of an operator associated with the grammar. Every boolean grammar can be transformed into an equivalent (under the new semantics) grammar in normal form. Based on this normal form, we propose an

Randomized and approximation algorithms for blue-red matching

{\mathcal{O}(n^3)}

Temporal stratification tests for linear and branching-time deductive databases

algorithm for parsing that applies to any such normalized boolean grammar. In summary, the main contribution of this paper is to provide a semantics which applies to all boolean grammars while at the same time retaining the complexity of parsing associated with this type of grammars.

An Algorithm for Querying Linked Data Using Map-Reduce

We introduce the Blue-Red Matching problem: given a graph with red and blue edges, and a bound w, find a maximum matching consisting of at most w edges of each color. We show that Blue-Red Matching is at least as hard as the problem Exact Matching (Papadimitriou and Yannakakis, 1982), for which it is still open whether it can be solved in polynomial time. We present an RNC algorithm for this problem as well as two fast approximation algorithms. We finally show the applicability of our results to the problem of routing and assigning wavelengths to a maximum number of requests in all-optical rings.

A game-theoretic characterization of Boolean grammars

We consider the problem of extending temporal deductive databases with stratified negation. We argue that the classical stratification test for deductive databases is too restrictive when one shifts attention to the temporal case. Moreover, as we demonstrate, the (more general) local stratification approach is impractical: detecting whether a temporal deductive database is locally stratified is shown to be co-NP hard (even if one restricts attention to programs that only use one predicate symbol and two constants). For these reasons we define temporal stratification, an intermediate notion between stratification and local stratification. We demonstrate that for the temporal deductive databases we consider, temporal stratification coincides with local stratification in certain important cases in which the latter is polynomial-time decidable. We then develop two algorithms for detecting temporal stratification. The first algorithm applies to linear-time temporal deductive databases and it is efficient and more general than existing approaches; however, the algorithm sacrifices completeness for efficiency since it does not cover the whole class of temporally stratified programs. The second algorithm applies to branching-time temporal deductive databases (which include as a special case the linear-time ones). This algorithm is more expensive from a computational point of view, but it covers the whole class of temporally stratified programs. We discuss the relative merits of the two algorithms and compare them with other existing approaches.