Showing papers in "Information Processing Letters in 1988"

On generating all maximal independent sets

Abstract: We present an algorithm that generates all maximal independent sets of a graph in lexicographic order, with only polynomial delay between the output of two successive independent sets. We also show that there is no polynomial-delay algorithm for generating all maximal independent sets in reverse lexicographic order, unless P=NP.

Dynamic program slicing

Abstract: A dynamic program slice is an executable subset of the original program that produces the same computations on a subset of selected variables and inputs. It differs from the static slice (Weiser, 1982, 1984) in that it is entirely defined on the basis of a computation. The two main advantages are the following: Arrays and dynamic data structures can be handled more precisely and the size of slice can be significantly reduced, leading to a finer localization of the fault. The approach is being investigated as a possible extension of the debugging capabilities of STAD, a recently developed System for Testing and Debugging (Korel and Laski, 1987; Laski, 1987).

A faster approximation algorithm for the Steiner problem in graphs

Abstract: We present a new implementation of the Kou, Markowsky and Berman algorithm for finding a Steiner tree for a connected, undirected distance graph with a specified subset S of the set of vertices V . The total distance of all edges of this Steiner tree is at most 2(1-1/ l ) times that of a Steiner minimal tree, where l is the minimum number of leaves in any Steiner minimal tree for the given graph. The algorithm runs in O(| E |+| V |log| V |) time in the worst case, where E is the set of all edges and V the set of all vertices in the graph.

On computing a conditional edge-connectivity of a graph

Abstract: The conditional edge-connectivity λ ( G : P ) of a graph G ( V , E ) has been defined by Harary as the minimum cardinality | S | of a set S of edges such that G – S is disconnected and every component of G – S has the given graph property P . I n this article we present lower and upper bounds for λ( G : P ) when P is defined as follows: A graph H satisfies property P if it contains more than one vertex. We then present a polynomial-time algorithm for the computation of λ( G : P ). A new generalization of the notion of connectivity is also given.

Cryptographic implementation of a tree hierarchy for access control

Abstract: A cryptographic implementation is proposed for access control in a situation where users and information items are classified into security classes organized as a rooted tree, with the most privileged security class at the root. Each user stores a single key of fixed size corresponding to the user's security class. Keys for security classes in the subtree below the user's security class are generated from this key by iterative application of one-way functions. New security classes can be defined without altering existing keys. The scheme proposed here is based on conventional cryptosystems (as opposed to public key cryptosystems).

Optimum watchman routes

Abstract: In this paper we consider the problem of finding shortest routes from which every point in a given space is visible (watchman routes). We show that the problem is NP-hard in polygons with holes and we present an O(n loglog n) algorithm to find a shortest route in simple rectilinear polygons.

LTUR: a simplified linear-time unit resolution algorithm for Horn formulae and computer implementation

Abstract: Testing for the satisfiability of a Horn expression in propositional calculus is a fundamental problem in the area of logic programming for many reasons. Among these is the fact that the basic solution techniques for propositional Horn formulae have been shown to be central to the design of efficient interpreters for some predicate logic-based languages such as Hornlog (Gallier and Raatz, 1987). The present paper proposes a simplified way of deriving a linear-time algorithm avoiding many of the intricacies of previously known descriptions. In addition, a full, ready-to-use computer code is provided at the end of the paper together with a detailed analysis of the necessary data structures.

Paw-fee graphs

Abstract: We give decomposition theorem for a class of graphs and show how this theorem suggests efficient algorithms to optimize this class of graphs.

A unified approach to domination problems on interval graphs

Abstract: Une propriete tres simple des graphes intervalle est utilisee dans la realisation d'algorithmes a temps lineaire, developpes pour la resolution de differents problemes de domination

Finding paths and deleting edges in directed acyclic graphs

Abstract: Significant progress has recently been made in the design of efficient dynamic data structures for the representation of graphs. The data structures support the efficient insertion and/or deletion of edges in a graph, in addition to certain types of queries for the graph [2-5,7-15,17,18]. D_ynamic data structures of this nature are very useful for the on-line computation of graph properties and related problems. In particular, much attention has been devottj to the on-line computation of the connected components of graphs [4,5,7,8,10,11,13,14,15,17]. As far as undirected graphs are concerned, the algorithm proposed by Even and Shiloach [4] answers q questions about the existence of a path between two nodes while deleting an arbitrary number of edges in a graph with m edges and n nodes in 0( q + mn) time. A more general version of this problem has been discussed in [7], in which O(n) time for each insertion or deletion of edges was realized. Recently, Frederickson IS] improved this bound to O(G). In case of directed graphs, the on-line computation of the transitive closure was first tackled by Ibaraki and Katoh [8], who proposed an algorithm for maintaining the transitive closure of a digraph with n nodes and m edges in: * 0(n3) time for an arbitrary number of edge insertions, l O(n*(m + n)) time for an arbitrary number of edge deletions. In [lo], a data structure was introduced supporting both path retrieval operations and insertions of edges in O(n) amortized [16] time, thus improving the time required to maintain the transitive closure of a digraph during m edge insertions from 0(n3) to 0( mn). This data structure enables one not only to answer the question whether two nodes are connected in constant time but also to return a path between any couple of nodes in O(I) time, where I is the length of the achieved path. In this paper we restrict ourselves to directed acyclic graphs (DAGs), and show how to return an arbitrarily chosen path between couples of nodes (if it exists) during the deletion of edges in ark efficient manner. Thus, we are given a DAG G = (V, E) with n nodes and m edges and we want to perform on it a sequence of intermixed operations of the. following two hinds:

Optimal node ranking of trees

Abstract: We discuss the problem of ranking nodes of a tree, which is a restriction of the general node coloring problem. A tree is said to have rank number k if its vertices can be ranked using the integers 1, 2,…,k such that if two nodes have the same rank i, then there is a node with rank greater than i on the path between the two nodes. The optimal rank number of a tree gives the minimum height of its node separator tree. We present an O(n log n) algorithm for optimal node ranking of trees.

Are there interactive protocols for CO-NP languages?

Abstract: Etude du probleme consistant a determiner quels types de langage peuvent traiter des protocoles interactifs

An optimally efficient selection algorithm

Abstract: We give an optimally efficient parallel algorithm for selection on the EREW PRAM. It requires a linear number of operations and O(log n log ∗ n) time. A modification of the algorithm runs on the CRCW PRAM. It requires a linear number of operations and O(log n log ∗ /log log n) time.

Short propositional formulas represent nondeterministic computations

Abstract: A weaker form of the above result first appeared in [l], where it was used to show that CNF satisfiability is NP-hard. The theorem in [l] referred only to single-tape machines, and the length bound on the formula was something like T(n)3. The length bound was improved to T(n) log T(n) by Robson [4]. Recently, Steams and Hunt [6] have given a different construction which yields a slightly longer formula, namely one of length O(T(n) log2T(n)), but which applies to multitape Turing machines. All of the above constructions are fairly elaborate. The theorem is interesting because it gives information about the relative complexity of different NP problems. For example, Schnorr [5] uses it to show that SAT is quasilinear complete, and hence so are a number of other standard NP-complete problems. Stearns and Hunt [6] use it to show that, assuming SAT h.as asymptotic complexity 2”, many standard NP-complete problems have about the same complexity as SAT, but others, such as the CLIQUE problem, are easier. Dewdney [2] is interested because of its potential application to his generic reduction computer, which irnplements nondeterministic algorithms.

A linear algorithm to solve fixed-point equations on transition systems

Abstract: This paper gives an algorithm to compute the least fixed-point of a system of equations over a transition system. This algorithm has a time complexity linear in the size of the transition system, thus improving the known algorithms which are quadratic.

An improved parallel algorithm that computes the BFS numbering of a directed graph

Abstract: This paper presents a parallel algorithm that computes the breadth-first search (BFS) numbering of a directed graph in O(log2n) time using M(n) processors on the exclusive-read exclusive-write (EREW) parallel random access machine (PRAM) model, where M(n) denotes the number of processors needed to multiply two n x n integer matrices over the ring ( Z , +, x) in O(log n) time. The best known bound for M(n) is O(n2.376) (Coppersmith and Winograd, 1987). The algorithm presented in their paper uses fewer processors than the classical algorithm for BFS that employs matrix powering over the semiring (dioid) ( N , min, +), using O(log n) time and O(n3) processors on the concurrent-read concurrent-write (CRCW) model, or using O(log2 n) time and n3⧸log n processors on the EREW model.

Grammatical interface for even linear languages based on control sets

Abstract: We show that the grammatical inference problem for even linear languages is reduced to the problem for regular sets.

Yet another distributed depth-first-search algorithm

Abstract: A new distributed depth-first-search algorithm is presented whose communication and time complexities are bounded by 3|E| and 2|V|, respectively.

Data refinement by miracles

Abstract: Data refinement is the transformation in a computer program of one data type to another. Usually, we call the original data type “abstract”, and the final data type “concrete”. The concrete data type is said to represent the abstract.

Minimum-cost spanning tree as a path-finding problem

Abstract: In this paper we show that the minimum-cost spanning tree is a special case of the closed semiring path-finding problem. This observation gives us a nonrecursive algorithm for finding minimum-cost spanning trees on mesh-connected computers which has the same asymptotic running time as but is much simpler than the previous recursive algorithms.

Plane-sweep solves the closest pair problem elegantly

Abstract: Optimal algorithms for the closest pair problem are often complex because they are derived from algorithms that solve more general problems, such as all-nearest-neighbors or computing the Voronoi diagram. The only known direct algorithm with optimal worst-case time complexity (in the algebraic decision tree model of computation) uses divide-and-conquer and involves a complicated merge step. We show how the two-dimensional closest pair problem is solved elegantly in asymptotically optimal time using a plane-sweep algorithm which is easier to understand and implement. We explain why sweeping generalizes easily, but not efficiently, to multi-dimensional closest pair problems.

Proving open properties by induction

Abstract: Well-founded orders are the opposite of noetherian orders: every nonempty subset contains at least one minimal element. And a set is well-ordered when it is totally ordered by a wellfounded order: every nonempty set contains exactly one minimal element. Sofar, noetherian induction has been the most powerful way of proving properties inductively; it is indeed the most general one in the precise sence.

Generating t -ary trees in A-order

Abstract: Two ‘natural’ orders have been defined on the set of t-ary trees. Zaks (1980) referred to these orders as A-order and B-order. Many algorithms have been developed for generating binary and t-ary trees in B-order. Here we develop an algorithm for generating all t-ary trees with n nodes in (reverse) A-order, as well as ranking and unranking algorithms. The generation algorithm produces each tree in constant average time. The analysis of the generation algorithm makes use of an interesting bijection on the set of t-ary trees. The ranking algorithm runs in O(tn) time and the unranking algorithm in O(tn lg n) time.

Computing the determinant and the characteristic polynomial of a matrix via solving linear systems of equations

Abstract: We combine Cramer's rule, p -adic lifting, and rational interpolation in an unusual way, in order to reduce the problems of computing the determinant, det A , and all other coefficients of the characteristic polynomial, det(λ I - A ), of a matrix A to inverting A and⧸or to solving linear systems of equations. Such a reduction enables us to apply Hensel's effective p -adic lifting to the evaluation of det A and det(λ I - A ); from that practically important point of view, no comparable alternative is known. On the theoretical side, no other ways of reduction of computing det A to solving few linear systems are known.

Polynomially solvable satisfiability problems

Abstract: We address the well-known satisfiability problem (SAT), ie, the problem of checking whether a given propositional formula is satisfiable Although the general satisfiability problem is NP-complete, some particular cases of SAT are known to be easy The most important of those cases is HORN-SAT, ie, the satisfiability problem in the case of Horn clauses: actually, an instance of HORN-SAT can be solved in linear time Yamasaki and Doshita (1983) have introduced a new subclass of SAT, S0, which is polynomially solvable and which strictly includes HORN-SAT Here we introduce a family of subclasses of SAT, Γ0, Γ1,…,Γk,…, such that HORN-SAT = Γ0, S0 = Γ1, Γk ⊇ Γk-1, k = 1,2,…, and Γk approaches to SAT as k increases For each k, Γk is solvable in O(n∗nk) time, where n is the number of propositional letters, m is the number of clauses, and n∗ = O(nm) is the size of the input An algorithm to check whether a given instance of SAT belongs to Γk, for any k, which runs in O(n∗nk time, is also described