Showing papers in "Discrete Applied Mathematics in 2003"

TL;DR: In this paper, it was shown that the maximum edge biclique problem in bipartite graphs is NP-complete. But the problem is not NP-hard in general graphs.

TL;DR: Three simple and natural greedy algorithms for the maximum weighted independent set problem are considered and it is shown that two of them output an independent set of weight at least Σv∈V(G) W(v)/[d(v) + 1].

TL;DR: The first polynomial algorithms for chromatic number, edge-dominating set and list-q-coloring with costs (fixed number of colors q) are presented, both vertex and edge versions of three graph partitioning problems.

TL;DR: In this paper, the authors present a survey of properties of the lattice of closure systems on a finite set S with proofs of the more significant results, including that this lattice is atomistic and lower bounded.

TL;DR: The problem of simultaneously locating obnoxious facilities and routing obnoxious materials between a set of built-up areas and the facilities is addressed and an effective Branch and Bound algorithm is presented, which aims at reducing the gap between the lower and upper bounds.

TL;DR: This work proves that a T-graph has an efficient dominating set if and only if T is a star, and gives a constructing tool to produce E-chains of Cayley graphs on symmetric groups.

TL;DR: It is proved for positive integers k and q that every (kq)-edge-connected hypergraph of rank q can be decomposed into k connected sub-hypergraphs, and a connectivity-type sufficient condition for the existence of k edge-disjoint Steiner trees in a bipartite graph.

TL;DR: The parameterized complexity of the vertex colouring problem on F + ke, F - ke and F - kv for various families F of graphs is shown to be fixed-parameter tractable and solvable in polynomial time for each fixed k but W[1]-hard for split + kv graphs.

TL;DR: It is shown that in a class X defined by a finite set of forbidden induced subgraphs, the problem is NP-hard if and only if X includes a boundary class.

TL;DR: This paper classifies all cyclic codes over Z4 of length 2n,n odd in terms of discrete Fourier transforms, generator polynomials, parity check matrices, and the concatenated (a + b|b) construction.

TL;DR: This paper improves the running time of Schrijver's algorithm by designing a push-relabel framework for submodular function minimization (SFM), and extends this algorithm to carry out parametric minimization for a strong map sequence of sub modular functions in the same asymptotic running time as a single SFM.

TL;DR: An extension to the classical vehicle routing problem where vehicles can be assigned more than one route within a working time period is investigated and a multi-phase constructive heuristic, which is enhanced by suitable data structure, is proposed.

TL;DR: Efficient techniques for computing a molecular surface boundary representation as a set of non-uniform rational B-splines patches are introduced, which introduces for molecules the same geometric data structure used in the solid modeling community and enables immediate access to a wide range of modeling operations and techniques.

TL;DR: The scope of certain well-studied polynomial-time solvable classes of Satisfiability is investigated and it is found that the matched formulas are more numerous than Horn, extended Horn, renamable Horn, q-Horn, CC-balanced, or single lookahead unit resolution (SLUR) formulas.

TL;DR: The main result is that a dichotomy holds (subject to the assumption P ≠ NP), which is, for a considered class A, the problem is either (1) NP-complete, or (2) it can be solved in linear time.

TL;DR: This paper presents an exact algorithm solving MAX-2-SAT in time poly(L) ċ 2K/5, where K is the number of clauses and L is their total length, and derives upper bounds for the (MAX-SNP-complete) maximum cut problem ( MAX-CUT), showing that it can be solved in timepoly(M) Ċ 2M/3, where M is thenumber of edges in the graph.

TL;DR: This work considers the problem of interconnecting a set of customer sites using bidirectional SONET rings of equal capacity and presents exact, integer-programming based solution techniques and fast heuristic algorithms for this problem.

TL;DR: This paper focuses on how similar questions can be asked about hypergraphs, and it is shown that often the answers are also similar many known graph orientation theorems can be extended to hyper graphs, using the familiar uncrossing techniques.

TL;DR: It is proved that the edge sum coloring and the edge strength problems are both NP-complete for k-regular graphs, k ≥ 3 and also a polynomial time algorithm is given to solve the edgeSum coloring problem on trees.

TL;DR: The notion of an autarky system A is introduced, which detects deletion of superfluous clauses from a clause-set F and yields a canonical normal form NA(F) ⊆ F, a natural weakening of minimally unsatisfiable clause-sets opening the possibility for combinatorial approaches and including also satisfiable instances.

TL;DR: A polynomial time approximation algorithm with worst case performance guarantee arbitrarily close to the golden ratio ½(1 + √5) ≈ 1.61803 is given.

TL;DR: Two new characterizations of M- and M'-convex functions are given generalizing Gul and Stacchetti's results on the equivalence among the single improvement condition, the gross substitutes condition and the no complementarities condition for set functions.

TL;DR: A fairly complete computational complexity classification is obtained, and a number of polynomial-time algorithms are designed to solve scheduling problems for parallel dedicated machines subject to resource constraints.

TL;DR: Evidence is given of theoretical and empirical evidence that QSATCNF is often faster than Davis and Putnam-type satisfiability checkers and ordered binary decision diagrams (OBDDs) on this class of formulae and an example where QS ATC NF is exponentially faster than BDDs is given.

TL;DR: This paper proposes a linear-time algorithm for finding a maximum induced matching in a bipartite permutation (bipartite AT-free) graph using the greedy approach and shows that using the same technique the minimum chain subgraph cover problem on bipartites permutation graphs can be solved with the same time complexity.

TL;DR: A fast method to compute random powers andMultiples in certain important situations including powers in the Galois field F2n, multiples on Koblitz elliptic curves, and multiples in NTRU convolution polynomial rings is described.

TL;DR: A complete classification of (P5,co-chair,H)-free graphs with respect to their clique width is given and implies linear time algorithms for all algorithmic problems expressible in LinEMSOL--a variant of Monadic Second Order Logic including the MWS Problem.

TL;DR: It is shown that single-facility location problems on a network with uncertain edge lengths are strongly NP-hard, in contrast with robust location problems with only node weights uncertainty that are known to be polynomially solvable.

TL;DR: Graph property P(x1,...,xk) is a graph property expressible in monadic second-order logic, and clique-width is a complexity measure on graphs similar to tree- width, but more powerful since every set of graphs of bounded tree-width has bounded cliques-width, but not conversely.

TL;DR: The paper reviews some of the existing exact bounds to the maximum clique of a graph and successively presents a new upper and a new lower bound that improves strictly the present best lower bound published by Wilf.