Karl Abrahamson

Bio: Karl Abrahamson is an academic researcher from Washington State University. The author has contributed to research in topics: Randomized algorithm & Probabilistic logic. The author has an hindex of 12, co-authored 29 publications receiving 1131 citations. Previous affiliations of Karl Abrahamson include East Carolina University & University of Washington.

Generalized string matching

Abstract: Given a pattern string of length n and an object string of length m, the string matching problem asks for the positions of all occurrences of the pattern in the object string. This paper investigates a generalization of string matching, in which the pattern is a sequence of pattern elements, each compatible with a set of symbols. The alphabet of symbols is infinite, with its members encoded in a finite alphabet. In contrast to standard string matching, which can be solved in simultaneous linear time and constant space, it is shown that generalized string matching requires a time-space product of $\Omega ({{n^2 } / {\log n}})$ on a powerful model of computation, when the alphabet is restricted to n symbols. Our proof uses a method of Borodin. The obvious algorithm for generalized string matching requires time $O(NM)$, where N is the length of the encoding of the pattern, and M is that of the object string. We describe an algorithm which solves generalized string matching in time $O(N + M + mN^{{1 / 2}} {\o...

On achieving consensus using a shared memory

Abstract: Chor, Israeli and Li recently published three randomized algorithms for a version of the consensus problem for a shared memory model of distributed computing. Their model requires, as atomic instructions on the shared memory, reads and random writes (in which a random choice and a write are done together in a single atomic instruction). This paper develops randomized algorithms for a model in which the only atomic operations on the shared memory are reads and writes.

Fixed-Parameter Intractability II (Extended Abstract)

Abstract: We describe new results in parameterized complexity theory, including an analogue of Ladner's theorem, and natural problems concerning k-move games which are complete for parameterized problem classes that are analogues of P-space.

Distributed algorithms

Abstract: In Distributed Algorithms, Nancy Lynch provides a blueprint for designing, implementing, and analyzing distributed algorithms. She directs her book at a wide audience, including students, programmers, system designers, and researchers. Distributed Algorithms contains the most significant algorithms and impossibility results in the area, all in a simple automata-theoretic setting. The algorithms are proved correct, and their complexity is analyzed according to precisely defined complexity measures. The problems covered include resource allocation, communication, consensus among distributed processes, data consistency, deadlock detection, leader election, global snapshots, and many others. The material is organized according to the system model-first by the timing model and then by the interprocess communication mechanism. The material on system models is isolated in separate chapters for easy reference. The presentation is completely rigorous, yet is intuitive enough for immediate comprehension. This book familiarizes readers with important problems, algorithms, and impossibility results in the area: readers can then recognize the problems when they arise in practice, apply the algorithms to solve them, and use the impossibility results to determine whether problems are unsolvable. The book also provides readers with the basic mathematical tools for designing new algorithms and proving new impossibility results. In addition, it teaches readers how to reason carefully about distributed algorithms-to model them formally, devise precise specifications for their required behavior, prove their correctness, and evaluate their performance with realistic measures. Table of Contents 1 Introduction 2 Modelling I; Synchronous Network Model 3 Leader Election in a Synchronous Ring 4 Algorithms in General Synchronous Networks 5 Distributed Consensus with Link Failures 6 Distributed Consensus with Process Failures 7 More Consensus Problems 8 Modelling II: Asynchronous System Model 9 Modelling III: Asynchronous Shared Memory Model 10 Mutual Exclusion 11 Resource Allocation 12 Consensus 13 Atomic Objects 14 Modelling IV: Asynchronous Network Model 15 Basic Asynchronous Network Algorithms 16 Synchronizers 17 Shared Memory versus Networks 18 Logical Time 19 Global Snapshots and Stable Properties 20 Network Resource Allocation 21 Asynchronous Networks with Process Failures 22 Data Link Protocols 23 Partially Synchronous System Models 24 Mutual Exclusion with Partial Synchrony 25 Consensus with Partial Synchrony

Parameterized Complexity

Abstract: An approach to complexity theory which offers a means of analysing algorithms in terms of their tractability. The authors consider the problem in terms of parameterized languages and taking "k-slices" of the language, thus introducing readers to new classes of algorithms which may be analysed more precisely than was the case until now. The book is as self-contained as possible and includes a great deal of background material. As a result, computer scientists, mathematicians, and graduate students interested in the design and analysis of algorithms will find much of interest.

Epidemic algorithms for replicated database maintenance

Abstract: Whru a dilt~lhSC is replicated at, many sites2 maintaining mutual consistrnry among t,he sites iu the fac:e of updat,es is a signitirant problem. This paper descrikrs several randomized algorit,hms for dist,rihut.ing updates and driving t,he replicas toward consist,c>nc,y. The algorit Inns are very simple and require few guarant,ees from the underlying conllllunicat.ioll system, yc+ they rnsutc t.hat. the off(~c~t, of (‘very update is evcnt,uwlly rf+irt-ted in a11 rq1ica.s. The cost, and parformancc of t,hr algorithms arc tuned I>? c%oosing appropriat,c dist,rilMions in t,hc randoinizat,ioii step. TIN> idgoritlmls ilr(’ c*los~*ly analogoIls t,o epidemics, and t,he epidcWliolog)litc\ratiirc, ilitlh iii Illld~~rsti4lldill~ tlicir bc*liavior. One of tlW i$,oritlims 11&S brc>n implrmcWrd in the Clraringhousr sprv(brs of thr Xerox C’orporat~c~ Iiitcrnc4, solviiig long-standing prol>lf~lns of high traffic and tlatirl>ilsr inconsistcllcp.

Parallel algorithms for shared-memory machines

Abstract: Publisher Summary This chapter discusses parallel algorithms for shared-memory machines. Parallel computation is rapidly becoming a dominant theme in all areas of computer science and its applications. It is estimated that, within a decade, virtually all developments in computer architecture, systems programming, computer applications and the design of algorithms will be taking place within the context of parallel computation. In preparation for this revolution, theoretical computer scientists have begun to develop a body of theory centered on parallel algorithms and parallel architectures. As there is no consensus yet on the appropriate logical organization of a massively parallel computer, and as the speed of parallel algorithms is constrained as much by limits on interprocessor communication as it is by purely computational issues, it is not surprising that a variety of abstract models of parallel computation have been pursued. Closest to the hardware level are the VLSI models, which focus on the technological limits of today's chips, in which gates and wires are packed into a small number of planar layers.

Fast text searching: allowing errors

Abstract: T h e string-matching problem is a very c o m m o n problem. We are searching for a string P = PtP2. . "Pro i n s i d e a la rge t ex t f i le T = t l t2. . . t . , b o t h sequences of characters from a f i n i t e character set Z. T h e characters may be English characters in a text file, DNA base pairs, lines of source code, angles between edges in polygons, machines or machine parts in a production schedule, music notes and tempo in a musical score, and so fo r th . We w a n t to f i n d a l l occurrences of P i n T; n a m e l y , we are searching for the set of starting posit ions F = {i[1 --i--n m + 1 s u c h t h a t titi+ l " " t i + m 1 = P } " T h e two most famous algorithms for this problem are t h e B o y e r M o o r e algorithm [3] and t h e K n u t h Morris Pratt algorithm [10]. There are many extensions to t h i s problem; for example, we may be looking for a set of patterns, a pattern w i t h "wi ld cards," or a regular expression. String-matching tools are included in every reasonable text editor, word processor, and many other applications.