Abstract: A new and simple method is proposed for finding good encoders both for channels and for sources with side information. This method relies on the continuous version of a graph decomposition result of Lovasz. The presently known best exponential error bounds for both problems follow in a unified manner with an improvement on the source coding bound. The previous bounds for universal codes of the authors and Marton are also improved.

Abstract: Fault- tolerant characteristics of a Boolean n cube array of microprocessors are analyzed. Connectivity properties of the network graph are used to show that n processor or link failures are required to isolate a processor. For processor failures the network is shown to be n (one step) diagnosable. A testing algorithm is presented which can diagnose up to n processor failures.

Abstract: We present a heuristic algorithm for partitioning the nodes of a graph into a given number of subsets in such a way that the number of edges connecting the various subsets is a minimum. The sizes of the subsets must be specified in advance.

Abstract: The purpose of this paper is to present the problem of scheduling the games of a hockey or football league. It is shown how a graph theoretical model may be used and how some constraints related to the alternating pattern of home-games and away-games can be handled. Finally some other requirements occurring in practice are also discussed and introduced into the model.

Abstract: Given a planar graph, we wish to draw it in the plane so that no edges cross. We might be given a particular planarisation (a specification giving the faces of the desired drawing) instead of merely the graph, but this is not required. Given a planarisation and a choice of outermost face, all drawings are in a sense equivalent; indeed, when the drawing is performed on the surface of a sphere instead of on the plane, even the choice of outermost face is irrelevant. To make the problem meaningful, we must introduce further constraints. Two general forms of constraints are: (1) absolute restrictions on the details of the drawing, that is, disallowing or requiring certain features, and (2) weighted restrictions, that is, additional objectives to be met to whatever extent is possible. We first examine the general problem, and look at various constraints that have been found to yield useful drawings in some applications. We then examine in more detail one particular set of constraints, developing a fast algorithm for producing drawings meeting those constraints, and proving some theorems relating to the overall complexity of the problem. Finally, we look at what results are known regarding other variations on the general problem.

Abstract: Finding the solution of a dynamic programming problem m the form of polyadlc funcUonal equatmns is shown to be equivalent to searching a mmmaal cost path in an AND/OR graph with monotone cost functions The proof is given in an algebraic framework and is based on a commutaUvity result between solutton and mterpretauon of a symbohc system This approach Is simdar to the one used by some authors to prove the eqmvalence between the operaUonal and denotatmnal semantics of programming languages

Abstract: We present a heuristic algorithm for partitioning the nodes of a graph into a given number of subsets in such a way that the number of edges connecting the various subsets is a minimum. The sizes of the subsets must be specified in advance.

Abstract: In this extended abstract, we present several new layouts for the shuffle-exchange graph, including one which requires only 0(n2/log2n) area. The optimal layout is described and analyzed in section 3. The analysis is heavily dependent on several combinatorial results which we state in section 2 and prove in the appendix. The other layouts are described in section 4. Although these layouts are not asymptotically optimal (most require 0(n2/log3/2n) area), the theory behind their development is interesting and may eventually lead to good practical layouts as well as other asymptotically optimal layouts.

Abstract: This paper presents a formalism for describing the behavior of computational networks at the algorithmic level. It establishes a direct correspondence between the mathematical expressions defining a function and the computational networks which compute that function. By formally manipulating the symbolic expressions that define a function, it is possible to obtain different networks that compute the function. From this mathematical description of a network, one can directly determine certain important characteristics of computational networks, such as computational rate, performance and communication requirements. The use of this formalism for design and verification is demonstrated on computational networks for Finite Impulse Response (FIR) filters, matrix operations, and the Discrete Fourier Transform (DFT). The progression of computations can often be modeled by wave fronts in an illuminating way. The formalism supports this model. A computational network can be viewed in an abstract form that can be represented as a graph. The duality between the graph representation and the mathematical expressions is briefly introduced.

Abstract: Recently I published several papers on finite and infinite combinatorial problems. I will try to make the overlap with this paper as small as possible ; as a result I have to omit some of my most interesting problems, but first of all I give some references to my older papers where these questions have been discussed P. Erdős, Old and new problems in combinatorial analysis and graph theory, Secondference). This paper contains extensive references to my previous papers. P. Erdős, Combinatorial problems which I would most like to see solved, will soon appear in the new Hungarian periodical Combinatorics. For applications of probabilistic methods to combinatorial analysis see our book, First I discuss problems connected with Ramsey's theorem and its generalisations, here I of course can not avoid overlap with previous papers. r(nl,. . .,nk) is the smallest integer for which if one colors the edges of K(r(nl,. . .,nk)) by k colors (K(t)

Abstract: After stating the weighted, perfect matching problem and briefly describing Edmonds' algorithm, certain postoptimality procedures are described. These procedures aid in reoptimizing related matching problems in which a few edge weights are altered. Regardless of the actual implementation of the matching algorithm used, when changing a single edge weight, the postoptimality procedures are on the order of cardinality (N) more efficient than solving the modified problem “from scratch,” where N is the node set of the underlying graph.

Abstract: The scaling of signal levels in multiple-feedback filters is presented in a systematic way, as an operation on a cutset of the corresponding signal-flow graph. This operation leads to an interesting summed sensitivity invariant.

Abstract: In this paper we present an example of a design for a “data structure chip” and suggest how it can be used for problem solving in a digital system. In particular, we describe a systolic structure which can be used, for a graph, to find the connected components, a spanning tree, or, when used in conjunction with a systolic priority queue, a minimum spanning tree.

Abstract: T. Parsons proposed and partially analyzed the following pursuit-evasion problem on graphs: A team of searchers traverse the edges of a graph G in pursuit of a fugitive, who moves along the edges of the graph with complete knowledge of the locations of the pursuers. What is the smallest number s(G) of searchers that will suffice for guaranteeing capture of the fugitive? We show that determining whether s(G) ≤ K, for a given integer K, is NP-hard for general graphs but can be solved in linear time for trees. We also provide a structural characterization of those graphs with s(G) ≤ K for K = 1,2,3.

Abstract: A model of VLSI computation suitable for the description of algorithms at a high level is introduced. The model is basically a language to express parallel computations which can be efficiently implemented by a VLSI circuit. This language is used to describe area-time e_fficient algorithms for a few well known graph prob­ lems. The exact complexity of these algorithms and their relevance to recent work on the inherent limita­ tions of VLSI computations are also presented.

Abstract: An indexing technique for text data based on word fragments is described In contrast to earlier approaches the fragments are allowed to be overlapping and are linked in a directed graph structure reflecting that many fragments (“Superstrings”) contain other fragments as substrings This leads to a redundant free set of primary data pointers By classifying the set of Superstrings belonging to a fragment according to the position of the fragment in the Superstring, one gains a novel possibility of supporting exact match-, partial match-, and masked partial match-retrieval by an index The search strategies for the various retrieval cases are described

Abstract: The scheduling problem for unit time task systems with arbitrary precedence constrainls is known to be NP-complete. We show that the same is true even if the precedence constraints are restricted to certain subclasses which make the corresponding parallel programs more structured. Among these classes are those derived from hierarchic cobegin-coend programming constructs, level graph forests, and the parallel or serial composition of an out-tree and an in-tree. In each case, the completeness proof depends heavily on the number of processors being part of the problem instances.