In this paper we present and describe an improved version of the Zero-Neighbors algorithm, which we call the Zero-Coverings algorithm. We also present a method for finding a smallest subset of codewords ( Zero-Coverings) which need to be stored to ...

Consider the problem of transporting a set of objects between the vertices of a simple graph by a vehicle that traverses the edges of the graph. The problem of finding a shortest tour for the vehicle to transport all objects from their initial vertices ...

In this paper we extend the notion of a ranking of elements in a weak order to a ranking of elements in general ordered sets. The weakness of an ordered set P = ( X ,\prec) (denoted wk ( P )) is the minimum integer k for which there exists an ...

The richest class of t-perfect graphs known so far consists of the graphs with no so-called odd- K . Clearly, these graphs have the special property that they are hereditary t-perfect in the sense that every subgraph is also t-perfect, but they are ...

Let G be an Eulerian digraph, and let {x₁, x₂}, {y₁,y₂} be two pairs of vertices in G. A directed path from a vertex s to a vertex t is called an st-path. An instance (G;{x₁, x₂}, {y₁,y₂}) is called feasible if there is a choice of h,i,j,k with {h,i} = {...

In many combinatorial situations there is a notion of independence of a set of points. Maximal independent sets can be easily constructed by a greedy algorithm, and it is of interest to determine, for example, if they all have the same size or the same ...

An input to the betweenness problem contains m constraints over n real variables (points). Each constraint consists of three points, where one of the points is specified to lie inside the interval defined by the other two. The order of the other two ...

Suppose G=(V,E) is a simple graph and k is a fixed positive integer. A vertex z k-neighborhood-covers an edge (x,y) if d(z,x) \leq k$ and d(z,y) \leq k$. A k-neighborhood-covering set is a set C of vertices such that every edge in E is k-...

Each of n processors has a value which should be transmitted to all other processors. This fundamental communication task is called gossiping . In a unit of time every processor can communicate with at most one other processor and during such a ...

Given a set of n nuts of distinct widths and a set of n bolts such that each nut corresponds to a unique bolt of the same width, how should we match every nut with its corresponding bolt by comparing nuts with bolts? (No comparison is allowed between ...

For every string inclusion relation there are two optimization problems: find a longest string included in every string of a given finite language, and find a shortest string including every string of a given finite language. As an example, the two well-...

There is a polynomial algorithm which finds a decomposition of any given 4-regular graph into two triangle-free 2-factors or shows that such a decomposition does not exist.

In this paper we describe new constructions for de Bruijn sequences and Perfect Factors. These constructions are all based upon the idea of constructing one sequence (or set of sequences) from another. As a result of this fact, the sequences obtained ...

We describe efficient algorithms for finding even cycles in undirected graphs. Our main results are the following: (i) For every $k \geq 2$, there is an $O(V^2)$ time algorithm that decides whether an undirected graph $G=(V,E)$ contains a simple cycle ...

For a family ${\cal F} \subseteq 3^E$ closed with respect to the reduced union and intersection and for a bisubmodular function $f: {\cal F}\rightarrow \mbox{\bf R}$ with $(\emptyset,\emptyset) \in \cal F$ and $f(\emptyset,\emptyset)=0$, the ...

We give a polynomial time algorithm for solving the Euclidean Steiner tree problem when the terminals are constrained to lie on a fixed finite set of disjoint finite-length compact simple smooth curves. The problem is known to be NP-hard in general. We ...

Generalizing the two-commodity flow theorem of Rothschild and Whinston [Oper. Res., 14 (1966), pp. 377--387] and the multiflow theorem of Lovász [Acta Mat. Akad. Sci. Hungaricae, 28 (1976), pp. 129--138] and Cherkasky [Ekonom.-Mat. Metody, 13 (1977), ...

In this paper we modify Buchberger's S-pair reduction algorithm for computing a Gröbner basis of a toric ideal so as to apply it to an integer program (IP) in inequality form with fixed right-hand sides and fixed upper bounds on the variables. We ...

Let $K=C\cup e_1\cup e_2$ be a subgraph of G consisting of a cycle C and disjoint paths e₁ and e₂ connecting two interlacing pairs of vertices in C. Suppose that K is embedded in the Möbius band in such a way that C lies on its boundary. An algorithm is ...