Martin Charles Golumbic

Last updated
Prof. Martin Charles Golumbic Martin Golumbic.jpg
Prof. Martin Charles Golumbic


Martin Charles Golumbic (born September 30, 1948) is a mathematician and computer scientist, best known for his work in algorithmic graph theory and in artificial intelligence. He is the founding editor-in-chief of the journal Annals of Mathematics and Artificial Intelligence, published by Springer. [1]

Contents

Biography

Golumbic was born in 1948 in Erie, Pennsylvania, U.S. He received his Ph.D. in 1975 at Columbia University, where his advisor was Samuel Eilenberg. [2] He was a professor at the Courant Institute of Mathematical Sciences of New York University until 1980, and then a researcher at Bell Laboratories until moving permanently to Israel in 1982, where he previously held positions at IBM Research and Bar-Ilan University. Golumbic is the founder and director emeritus of the Caesarea Edmond Benjamin de Rothschild Institute for Interdisciplinary Applications of Computer Science at the University of Haifa. He has held visiting positions at Université de Paris, the Weizmann Institute of Science, the École Polytechnique Fédérale de Lausanne, the Universidade Federal do Rio de Janeiro, Columbia University, Rutgers University, the Indian Institute of Technology Kharagpur, Tsinghua University, and the University of New South Wales.

Golumbic was elected a fellow of the Institute of Combinatorics and its Applications (1995), fellow of the European Association for Artificial Intelligence (2005), and member of the Academia Europaea, honoris causa (2013). Golumbic also served as chairman of the Israeli Association of Artificial Intelligence (1998–2004), and founded and chaired numerous international symposia in discrete mathematics and in the foundations of artificial intelligence.

He is the author of several books including Algorithmic Graph Theory and Perfect Graphs, Tolerance Graphs (with Ann Trenk) and Fighting Terror Online: The Convergence of Security, Technology, and the Law.

Scientific Contributions

Golumbic's work in graph theory lead to the study of new perfect graph families such as tolerance graphs, which generalize the classical graph notions of interval graph and comparability graph. He is credited with introducing the systematic study of algorithmic aspects in intersection graph theory, and initiated research on new structured families of graphs including the edge intersection graphs of paths in trees, tolerance graphs, chordal probe graphs and trivially perfect graphs. Golumbic, Kaplan and Shamir introduced the study of graph sandwich problems.

In the area of compiler optimization, Golumbic holds a joint patent with Vladimir Rainish, Instruction Scheduler for a Computer, (UK9-90-035/IS), an invention based on their technique called SHACOOF (ScHeduling Across COntrOl Flow), which in Hebrew means "transparent". He has contributed to the development of fundamental research in artificial intelligence in the area of complexity and spatial-temporal reasoning.

Honors and awards

Bibliography

Related Research Articles

Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.

Interval graph the intersection graph of a collection of intervals of the real line

In graph theory, an interval graph is an undirected graph formed from a set of intervals on the real line, with a vertex for each interval and an edge between vertices whose intervals intersect. It is the intersection graph of the intervals.

SPITBOL is a compiled implementation of the SNOBOL4 programming language. Originally targeted for the IBM System/360 and System/370 family of computers, it has now been ported to most major microprocessors including the SPARC. It was created by Robert Dewar and Ken Belcher, who were then at the Illinois Institute of Technology.

Perfect graph type of graph (mathematical structure)

In graph theory, a perfect graph is a graph in which the chromatic number of every induced subgraph equals the size of the largest clique of that subgraph. Equivalently stated in symbolic terms an arbitrary graph is perfect if and only if we have:

Chordal graph

In the mathematical area of graph theory, a chordal graph is one in which all cycles of four or more vertices have a chord, which is an edge that is not part of the cycle but connects two vertices of the cycle. Equivalently, every induced cycle in the graph should have exactly three vertices. The chordal graphs may also be characterized as the graphs that have perfect elimination orderings, as the graphs in which each minimal separator is a clique, and as the intersection graphs of subtrees of a tree. They are sometimes also called rigid circuit graphs or triangulated graphs.

Complement graph

In graph theory, the complement or inverse of a graph G is a graph H on the same vertices such that two distinct vertices of H are adjacent if and only if they are not adjacent in G. That is, to generate the complement of a graph, one fills in all the missing edges required to form a complete graph, and removes all the edges that were previously there. It is not, however, the set complement of the graph; only the edges are complemented.

Jack Edmonds American/Canadian mathematician and computer scientist

Jack R. Edmonds is an American-born and educated computer scientist and mathematician who lived and worked in Canada for much of his life. He has made fundamental contributions to the fields of combinatorial optimization, polyhedral combinatorics, discrete mathematics and the theory of computing. He was the recipient of the 1985 John von Neumann Theory Prize.

In graph theory, a comparability graph is an undirected graph that connects pairs of elements that are comparable to each other in a partial order. Comparability graphs have also been called transitively orientable graphs, partially orderable graphs, containment graphs, and divisor graphs. An incomparability graph is an undirected graph that connects pairs of elements that are not comparable to each other in a partial order.

Split graph

In graph theory, a branch of mathematics, a split graph is a graph in which the vertices can be partitioned into a clique and an independent set. Split graphs were first studied by Földes and Hammer, and independently introduced by Tyshkevich and Chernyak (1979).

In graph theory, a branch of mathematics, many important families of graphs can be described by a finite set of individual graphs that do not belong to the family and further exclude all graphs from the family which contain any of these forbidden graphs as (induced) subgraph or minor. A prototypical example of this phenomenon is Kuratowski's theorem, which states that a graph is planar if and only if it does not contain either of two forbidden graphs, the complete graph K5 and the complete bipartite graph K3,3. For Kuratowski's theorem, the notion of containment is that of graph homeomorphism, in which a subdivision of one graph appears as a subgraph of the other. Thus, every graph either has a planar drawing or it has a subdivision of one of these two graphs as a subgraph.

Distance-hereditary graph

In graph theory, a branch of discrete mathematics, a distance-hereditary graph is a graph in which the distances in any connected induced subgraph are the same as they are in the original graph. Thus, any induced subgraph inherits the distances of the larger graph.

Permutation graph graph whose vertices represent the elements of a permutation

In mathematics, a permutation graph is a graph whose vertices represent the elements of a permutation, and whose edges represent pairs of elements that are reversed by the permutation. Permutation graphs may also be defined geometrically, as the intersection graphs of line segments whose endpoints lie on two parallel lines. Different permutations may give rise to the same permutation graph; a given graph has a unique representation if it is prime with respect to the modular decomposition.

Trivially perfect graph

In graph theory, a trivially perfect graph is a graph with the property that in each of its induced subgraphs the size of the maximum independent set equals the number of maximal cliques. Trivially perfect graphs were first studied by but were named by Golumbic (1978); Golumbic writes that "the name was chosen since it is trivial to show that such a graph is perfect." Trivially perfect graphs are also known as comparability graphs of trees, arborescent comparability graphs, and quasi-threshold graphs.

In graph theory, a perfectly orderable graph is a graph whose vertices can be ordered in such a way that a greedy coloring algorithm with that ordering optimally colors every induced subgraph of the given graph. Perfectly orderable graphs form a special case of the perfect graphs, and they include the chordal graphs, comparability graphs, and distance-hereditary graphs. However, testing whether a graph is perfectly orderable is NP-complete.

In graph theory and computer science, the graph sandwich problem is a problem of finding a graph that belongs to a particular family of graphs and is "sandwiched" between two other graphs, one of which must be a subgraph and the other of which must be a supergraph of the desired graph.

Trapezoid graph

In graph theory, trapezoid graphs are intersection graphs of trapezoids between two horizontal lines. They are a class of co-comparability graphs that contain interval graphs and permutation graphs as subclasses. A graph is a trapezoid graph if there exists a set of trapezoids corresponding to the vertices of the graph such that two vertices are joined by an edge if and only if the corresponding trapezoids intersect. Trapezoid graphs were introduced by Dagan, Golumbic, and Pinter in 1988. There exists algorithms for chromatic number, weighted independent set, clique cover, and maximum weighted clique.

In graph theory, a branch of mathematics, an indifference graph is an undirected graph constructed by assigning a real number to each vertex and connecting two vertices by an edge when their numbers are within one unit of each other. Indifference graphs are also the intersection graphs of sets of unit intervals, or of properly nested intervals. Based on these two types of interval representations, these graphs are also called unit interval graphs or proper interval graphs; they form a subclass of the interval graphs.

In the mathematical area of graph theory, a chordal bipartite graph is a bipartite graph B = (X,Y,E) in which every cycle of length at least 6 in B has a chord, i.e., an edge that connects two vertices that are a distance > 1 apart from each other in the cycle. A better name would be weakly chordal and bipartite since chordal bipartite graphs are in general not chordal as the induced cycle of length 4 shows.

In graph theory, a tolerance graph is an undirected graph in which every vertex can be represented by a closed interval and a real number called its tolerance, in such a way that two vertices are adjacent in the graph whenever their intervals overlap in a length that is at least the minimum of their two tolerances. This class of graphs was introduced in 1982 by Martin Charles Golumbic and Clyde Monma, who used them to model scheduling problems in which the tasks to be modeled can share resources for limited amounts of time.

Ann Natalie Trenk is an American mathematician interested in graph theory and the theory of partially ordered sets, and known for her research on proper distinguishing colorings of graphs and on tolerance graphs. She is a professor of mathematics at Wellesley College.

References

  1. Martin Charles Golumbic (1990). "Editorial welcome". Annals of Mathematics and Artificial Intelligence. 1 (1–4): I–III. doi:10.1007/BF01531065.
  2. Martin Charles Golumbic at the Mathematics Genealogy Project