Ingo Schiermeyer
Technische Hochschule
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Featured researches published by Ingo Schiermeyer.
european symposium on algorithms | 1994
Ingo Schiermeyer
We describe and analyze a ”level-oriented” algorithm, called ”Reverse-Fit”, for packing rectangles into a unit-width, infinite-height bin so as to minimize the total height of the packing. For L an arbitrary list of rectangles, all assumed to have width no more than 1, let h OPT denote the minimum possible bin height within the rectangles in L can be packed, and let RF(L) denote the height actually used by Reverse-Fit. We will show that RF(L)≤2·h OPT for an arbitrary list L of rectangles.
computer science logic | 1992
Ingo Schiermeyer
In this paper we describe and analyse an improved algorithm for solving the 3-Satisfiability problem. If F is a boolean formula in conjunctive normal form with n variables and r clauses, then we will show that this algorithm solves the Satisfiability problem for formulas with at most three literals per clause in time less than O(1,579n).
workshop on graph theoretic concepts in computer science | 1993
Ingo Schiermeyer
In this paper we describe and analyze an improved algorithm for deciding the 3-Colourability problem. If G is a simple graph on n vertices then we will show that this algorithm tests a graph for 3-Colourability, i.e. an assignment of three colours to the vertices of G such that two adjacent vertices obtain different colours, in less than O(1.415n) steps.
Journal of Graph Theory | 1995
Ahmed Ainouche; Ingo Schiermeyer
Let G be a simple undirected graph of order n. For an independent set S ⊂ V(G) of k vertices, we define the k neighborhood intersections Si = {v ϵ V(G)&n92;S|N(v) ∩ S| = i}, 1 ≦ i ≦ k, with si = |Si|. Using the concept of insertible vertices and the concept of neighborhood intersections, we prove the following theorem.
Discrete Mathematics | 1993
Ingo Schiermeyer
The well-known closure concept of Bondy and Chvatal (1976) is based on degree sums of pairs of nonadjacent vertices. It generalizes six earlier sufficient degree conditions for hamiltonian graphs. Ainouche and Christofides (1987) introduced a more general concept which is called the 0-dual closure. We prove that this concept generalizes five sufficient conditions for hamiltonian graphs which are not generalized by the concept of Bondy and Chvatal (1976).
Discrete Mathematics | 1994
Haitze J. Broersma; Ingo Schiermeyer
The well-known closure concept of Bondy and Chvatal is based on degree-sums of pairs of nonadjacent (independent) vertices. We show that a more general concept due to Ainouche and Christofides can be restated in terms of degree-sums of independent triples. We introduce a closure concept which is based on neighborhood unions of independent triples and which also generalizes the closure concept of Bondy and Chvatal.
Lecture Notes in Computer Science | 1998
Ingo Schiermeyer
In this paper we study lower bounds and approximation algorithms for the independence number α(G) in k-clique-free graphs G. Ajtai et al. [1] showed that there exists an absolute constant c 1 such that for any k-clique-free graph G on n vertices and with average degree ¯d, α(G) ≥ c 1 log((log ¯d)/k)/d n
workshop on graph theoretic concepts in computer science | 1990
Ingo Schiermeyer
In 1976 Bondy and Chvatal introduced the k-closure Ck(G) of a graph and described an algorithm which constructs it in O(n4) time. We present an algorithm which requires O(n3) time. However, in the average case, Ck(G) is computed by this algorithm for almost all integers k (in the asymptotic sense) with O ≦ k ≦ 2n − 2 in O(n2) time. We next present a parallel algorithm which requires O(n2 log n) time. In the average case, this algorithm computes Ck(G) for almost all integers k in O(log n) parallel time.
workshop on graph-theoretic concepts in computer science | 1995
Ingo Schiermeyer
We present a polynomial time approximation algorithm to colour a 3-colourable graph G with 3f(n) colours, if G has minimum degree δ(G)≥αn/f(n), where Ω(1)≤f(n)<O(n) and α is a positive constant. We also discuss NP—completeness and #P—completeness of restricted k-Colourability problems.
Discrete Mathematics | 1994
Ingo Schiermeyer
Abstract We consider the k - SATISFIABILITY problem ( k -SAT): Given a family F of n clauses c 1 , …, c n in conjunctive normal form, each consisting of k literals corresponding to k different variables of a set of r ⩾ k 1 boolean variables, is F satisfiable? By k -SAT(> n 0 ) we denote the k -SAT problem restricted to families with n > n 0 ( r ) clauses. We prove that for each k ⩾3 and each integer l ⩾4 such that r ⩾ lk 2 , the k- SAT (>( r k ) (2 k −1−4/l)) problem is NP-complete.