Yehoshua Perl

A LINEAR RECOGNITION ALGORITHM FOR COGRAPHS

Cographs are the graphs formed from a single vertex under the closure of the operations of union and complement. Another characterization of cographs is that they are the undirected graphs with no induced paths on four vertices. Cographs arise naturally in such application areas as examination scheduling and automatic clustering of index terms. Furthermore, it is known that cographs have a unique tree representation called a cotree. Using the cotree it is possible to design very fast polynomial time algorithms for problems which are intractable for graphs in general. Such problems include chromatic number, clique determination, clustering, minimum weight domination, isomorphism, minimum fill-in and Hamiltonicity. In this paper we present a linear time algorithm for recognizing cographs and constructing their cotree representation.

Clustering and domination in perfect graphs

Abstract A k-cluster in a graph is an induced subgraph on k vertices which maximizes the number of edges. Both the k-cluster problem and the k-dominating set problem are NP-complete for graphs in general. In this paper we investigate the complexity status of these problems on various sub-classes of perfect graphs. In particular, we examine comparability graphs, chordal graphs, bipartite graphs, split graphs, cographs and κ-trees. For example, it is shown that the k-cluster problem is NP-complete for both bipartite and chordal graphs and the independent k-dominating set problem is NP-complete for bipartite graphs. Furthermore, where the k-cluster problem is polynomial we study the weighted and connected versions as well. Similarly we also look at the minimum k-dominating set problem on families which have polynomial k-dominating set algorithms.

Finding Two Disjoint Paths Between Two Pairs of Vertices in a Graph

^SSTnXcr. Gwen a graph G = (V, E) and four verttces s~, tx, s~, and t2, the problem of finding two disjoint paths, P~ from s~ to tt and P2 from s2 to t2, is considered This problem may arise as a transportation network problem and m printed clrcmts routing The relations between several vemons of the problem are discussed Efficient algorithms are gwen for the following special cases-acyche directed graphs and 3-connected planar and chordal graphs.

The complexity of finding maximum disjoint paths with length constraints

A discharge luminescence element array comprising a pair of parallel insulating plates and a separator entirely sealed between the pair of insulating plates in which a groove-like gas flow path is provided between one of the plates and the separator for evacuating and providing gas from and to discharge spaces defined by the separator and the pair of insulating plates.

The periodic balanced sorting network

A periodic sorting network consists of a sequence of identical blocks. In this paper, the periodic balanced sorting network, which consists of log <italic>n</italic> blocks, is introduced. Each block, called a balanced merging block, merges elements on the even input lines with those on the odd input lines. The periodic balanced sorting network sorts <italic>n</italic> items in <italic>O</italic>([log <italic>n</italic>]<supscrpt>2</supscrpt>) time using (<italic>n</italic>/2)(log <italic>n</italic>)<supscrpt>2</supscrpt> comparators. Although these bounds are comparable to many existing sorting networks, the periodic structure enables a hardware implementation consisting of only one block with the output of the block recycled back as input until the output is sorted. An implementation of our network on the shuffle exchange interconnection model in which the direction of the comparators are all identical and fixed is also presented.

Interpolation search—a log log N search

Interpolation search is a method of retrieving a desired record by key in an ordered file by using the value of the key and the statistical distribution of the keys. It is shown that on the average log logN file accesses are required to retrieve a key, assuming that the N keys are uniformly distributed. The number of extra accesses is also estimated and shown to be very low. The same holds if the cumulative distribution function of the keys is known. Computational experiments confirm these results.

Structural methodologies for auditing SNOMED.

SNOMED is one of the leading health care terminologies being used worldwide. As such, quality assurance is an important part of its maintenance cycle. Methodologies for auditing SNOMED based on structural aspects of its organization are presented. In particular, automated techniques for partitioning SNOMED into smaller groups of concepts based primarily on relationships patterns are defined. Two abstraction networks, the area taxonomy and p-area taxonomy, are derived from the partitions. The high-level views afforded by these abstraction networks form the basis for systematic auditing. The networks tend to highlight errors that manifest themselves as irregularities at the abstract level. They also support group-based auditing, where sets of purportedly similar concepts are focused on for review. The auditing methodologies are demonstrated on one of SNOMEDs top-level hierarchies. Errors discovered during the auditing process are reported.

Auditing as Part of the Terminology Design Life Cycle

OBJECTIVE To develop and test an auditing methodology for detecting errors in medical terminologies satisfying systematic inheritance. This methodology is based on various abstraction taxonomies that provide high-level views of a terminology and highlight potentially erroneous concepts. DESIGN Our auditing methodology is based on dividing concepts of a terminology into smaller, more manageable units. First, we divide the terminologys concepts into areas according to their relationships/roles. Then each multi-rooted area is further divided into partial-areas (p-areas) that are singly-rooted. Each p-area contains a set of structurally and semantically uniform concepts. Two kinds of abstraction networks, called the area taxonomy and p-area taxonomy, are derived. These taxonomies form the basis for the auditing approach. Taxonomies tend to highlight potentially erroneous concepts in areas and p-areas. Human reviewers can focus their auditing efforts on the limited number of problematic concepts following two hypotheses on the probable concentration of errors. RESULTS A sample of the area taxonomy and p-area taxonomy for the Biological Process (BP) hierarchy of the National Cancer Institute Thesaurus (NCIT) was derived from the application of our methodology to its concepts. These views led to the detection of a number of different kinds of errors that are reported, and to confirmation of the hypotheses on error concentration in this hierarchy. CONCLUSION Our auditing methodology based on area and p-area taxonomies is an efficient tool for detecting errors in terminologies satisfying systematic inheritance of roles, and thus facilitates their maintenance. This methodology concentrates a domain experts manual review on portions of the concepts with a high likelihood of errors.

Max-Min Tree Partitioning

The max-rain k-partition algorithm may be formulated as follows: Given a tree T with n edges and a nonnegative weight associated with each vertex, assign a cut to each of k distinct edges of T so as to maximize the weight of the lightest resulting connected subtree. An algorithm for this problem is presented which initially assigns all k cuts to one edge incident with a terminal vertex of T; thereafter the cuts are shifted from edge to adjacent edge on the basis of local information. An efficient implementation with complexity O(k 2. rd(T) + kn), where rd(T) is the number of edges in the radius of T, is described. An algorithm for a simpler problem, namely, the partitioning of Tinto the maximum number of connected components whose weight is bounded below, is then described. Combined with the technique of binary search, it yields an alternative algorithm for the max-rain k-partition problem with complexity dependent on the range of the given weights.

Representing the UMLS as an Object-oriented Database: Modeling Issues and Advantages

OBJECTIVE The Unified Medical Language System (UMLS) combines many well-established authoritative medical informatics terminologies in one knowledge representation system. Such a resource is very valuable to the health care community and industry. However, the UMLS is very large and complex and poses serious comprehension problems for users and maintenance personnel. The authors present a representation to support the users comprehension and navigation of the UMLS. DESIGN An object-oriented database (OODB) representation is used to represent the two major components of the UMLS-the Metathesaurus and the Semantic Network-as a unified system. The semantic types of the Semantic Network are modeled as semantic type classes. Intersection classes are defined to model concepts of multiple semantic types, which are removed from the semantic type classes. RESULTS The authors provide examples of how the intersection classes help expose omissions of concepts, highlight errors of semantic type classification, and uncover ambiguities of concepts in the UMLS. The resulting UMLS OODB schema is deeper and more refined than the Semantic Network, since intersection classes are introduced. The Metathesaurus is classified into more mutually exclusive, uniform sets of concepts. The schema improves the users comprehension and navigation of the Metathesaurus. CONCLUSIONS The UMLS OODB schema supports the users comprehension and navigation of the Metathesaurus. It also helps expose and resolve modeling problems in the UMLS.