International Journal of Foundations of Computer Science

The shortest path problem is a classical network problem that has been extensively studied. The problem of determining not only the shortest path, but also listing the K shortest paths (for a given integer K>1) is also a classical one but has not been studied so intensively, despite its obvious practical interest. Two different types of problems are usually considered: the unconstrained and the constrained K shortest paths problem. While in the former no restriction in considered in the definition of a path, in the constrained K shortest paths problem all the paths have to satisfy some condition – for example, to be loopless.

In this paper new algorithms are proposed for the uncontrained problem, which compute a super set of the K shortest paths. It is also shown that ranking loopless paths does not hold in general the Optimality Principle and how the proposed algorithms for the unconstrained problem can be adapted for ranking loopless paths.

We study the computational power of machines that specify their own acceptance types, and show that they accept exactly the languages that -reduce to NP sets. A natural variant accepts exactly the languages that -reduce to P sets. We show that these two classes coincide if and only if , where the latter class denotes the sets acceptable via at most one question to #P followed by at most a constant number of questions to NP.

In this paper we deal with the layout of Trivalent Cayley Interconnection Networks. Namely, we prove that a lower bound on their layout area is Ω(2^n-1× 2^n-1) and we exhibit some methods to lay these networks out in O(2^n-1× 2^n-1).

We piont out that these layout methods work for other networks decomposable into equal length cycles connected by following fixed rules.

The d–dimensional k-ary array is the d–fold Cartesian product graph of the path graph P_k with k vertices. We show that the (edge) isoperimetric number of is given by and identify the cardinalities and the structure of the isoperimetric sets. For odd k, the cardinalities of isoperimetric sets in are , whereas every isoperimetric set for k even has cardinality .

The concept of grouping in relational algebra is well-known from its connection to aggregation. In this paper we generalize the grouping notion by defining a simultaneous grouping of more than one relation, and we discuss the application of operations on grouping elements other than just arithmetic aggregation. Finally we show that this grouping mechanism can be added to relational algebra without increasing its computational power.

This paper introduces a new graph theoretical concept called strong precedence which is used to address the problem of scheduling instability is non-preemptive static list scheduling. Scheduling instability occurs when a reduction in task duration of one or more tasks causes other tasks to miss their deadline. This problem has been addressed in the past by introducing additional precedence constraints into the precedence graph representing the workload, or by limiting the depth the dispatchers scan at run-time. We present an alternative stabilization approach based on the concept of strong and weak precedence. By defining a strong precedence relation on selected subgraphs, the workload becomes inherently stable without requiring the introduction of new edges into the graph.

Babel and Olariu (1995) introduced the class of (q, t) graphs in which every set of q vertices has at most t distinct induced P₄s. Graphs of clique-width at most k were introduced by Courcelle, Engelfriet and Rozenberg (1993) as graphs which can be defined by k-expressions based on graph operations which use k vertex labels. In this paper we study the clique–width of the (q, t) graphs, for almost all possible combinations of q and t. On one hand we show that every (q, q - 3) graph for q ≥ 7, has clique–width ≤ q and a q–expression defining it can be obtained in linear time. On the other hand we show that the class of (q, q - 3) graphs for 4 ≤ q ≤ 6 and the class of (q, q - 1) graphs for q ≥ 4 are not of bounded clique-width.

The critical problem of finding efficient implementations for recursive queries with bound arguments offers many open challenges of practical and theoretical import. In particular, there is a need to find methods that are effective for the general case, such as non-linear programs, as well as for specialized cases, such as left-recursive linear programs. In this paper, we propose a novel approach that solves this problem for chain queries, i.e., for queries where bindings are propagated from arguments in the head to arguments in the tail of the rules, in a chain-like fashion. The method, called pushdown method, is based on the fact that a chain query can have associated a context-free language and a pushdown automaton recognizing this language can be emulated by rewriting the query as a particular factorized left-linear program. The proposed method generalizes and unifies previous techniques such as the 'counting' and 'right-, left-, mixed-linear' methods. It also succeeds in reducing many non-linear programs to query-equivalent linear ones.