competitive self stabilizing k clustering in this paper we give a silent self stabilizing algorithm for constructing a k clustering of any asynchronous connected network with unique ids our algorithm stabilizes in o n rounds using o log k log n space per process where n is the number of processes in the general case our algorithm constructs o nk k clusters if the network is a unit disk graph udg then our algorithm is 7 2552k o 1 competitive that is the number of k clusters constructed by the algorithm is at most 7 2552k o 1 times the minimum possible number of k clusters in any k clustering of the same network more generally if the network is an quasi unit disk graph qudg with approximation ratio then our algorithm is 7 2552 2k o competitive in case of tree networks our algorithm computes a k clustering with the minimum number of clusters our solution is based on the self stabilizing construction of a data structure called an mis tree a spanning tree of the network whose processes at even levels form a maximal independent set of the network the mis tree construction we use called lfmis is the time bottleneck of our k clustering algorithm as it takes n rounds in the worst case while the rest of the algorithm takes o d rounds where d is the diameter of the network we would like to improve that time to be o d but we show that our distributed mis tree construction is a p complete problem

parallel algorithms in graph theory planarity testing we present efficient o log 2 n parallel algorithms for two classical graph problems planarity testing and finding triconnected components the algorithms use only a polynomial number of processors previous algorithms used omega n operations regardless of the number of available processors

on the structure of hermitian codes and decoding for burst errors in this paper it is proved that hermitian code is a direct sum of concatenated reed solomon codes over gf q sup 2 based on this discovery first a new method for computing the dimension and tightly estimating the minimum distance of the hermitian code is derived secondly a new decoding algorithm which is especially effective in dealing with burst errors with complexity o n sup 5 3 is described finally some possible approaches for optimization of hermitian codes are discussed

the expressiveness of a family of finite set languages abstract in this paper we characterize exactly the complexity of a set based database language called srl which presents a unified framework for queries and updates by imposing simple syntactic restrictions on it we are able to express exactly the classes p and logspace we also discuss the role of ordering in database query languages and show that the hom operator of machiavelli language in ohori et al 1989 does not capture all the order independent properties

on deciding trace equivalences for processes abstract in this paper we investigate the complexity of deciding trace maximal trace and trace equivalences for finite state processes and recursively defined processes specified by normed context free grammars cfgs in greibach normal form gnf the main results are as follows 1 1 trace maximal trace and trace equivalences for processes specified by normed gnf cfgs are all undecidable for this class of processes the regularity problem with respect to trace maximal trace or trace equivalence is also undecidable moreover all these undecidability results hold even for locally unary processes for processes specified by unary gnf cfgs the maximal trace equivalence is 2 p complete while the trace equivalence is nl complete and the trace equivalence is decidable in polynomial time by a dynamic programming algorithm 2 2 trace maximal trace and trace equivalences for finite state processes are pspace complete this holds even for locally unary finite state processes for unary finite state processes the maximal trace equivalence is co np complete while trace and trace equivalences are nl complete

the iterated mod problem abstract the iterated mod problem is this given a b1 b2 bn all integers or all polynomials in q x is a mod b1 mod b2 mod bn 0 when the inputs are integers we prove the problem p complete with respect to log space reductions whereas in the polynomial case we prove the problem is in nc the significance of these results lies primarily in the similarity between the iterated mod problem and the euclidean algorithm we also show that the superincreasing knapsack problem is p complete using a very similar proof

a note on the complexity of deciding bisimilarity of normed unary processes we give nc1 reduction of bisimulation equivalence for general normed context free processes to the same problem for normed unary context free processes

on deciding readiness and failure equivalences for processes in this paper we study the complexity of deciding readiness and failure equivalences for finite state processes and recursively defined processes specified by normed context free grammars cfgs in greibach normal form gnf the results are as follows 1 readiness and failure equivalences for processes specified by normed gnf cfgs are both undecidable for this class of processes the regularity problem with respect to failure or readiness equivalence is also undecidable moreover all these undecidability results hold even for locally unary processes in the unary case these problems become decidable in fact they are p2 complete we also show that with respect to bisimulation equivalence the regularity for processes specified by normed gnf cfgs is nl complete 2 readiness and failure equivalences for finite state processes are pspace complete this holds even for locally unary finite state processes these two equivalences are co np complete for unary finite state processes further for acyclic finite state processes readiness and failure equivalences are co np complete and they are nl complete in the unary case 3 for finite tree processes we show that finite trace readiness and failure equivalences are all l complete further the results remain true for the unary case our results provide a complete characterization of the computational complexity of deciding readiness and failure equivalences for several important classes of processes

bounded size dictionary compression sc k completeness and nc algorithms we study the parallel complexity of a bounded size dictionary version lru deletion heuristic of the lz2 compression algorithm the unbounded version was shown to be p complete when the size of the dictionary is o logk n the problem of computing the lz2 compression is shown to be hard for the class of problems solvable simultaneously in polynomial time and o logk n space that is sck we also introduce a variation of this heuristic that turns out to be an sck complete problem the original heuristic belongs to sck 1 in virtue of these results we argue that there are no practical parallel algorithms for lz2 compression with lru deletion heuristic or any other heuristic deleting dictionary elements in a continuous way for simpler heuristics swap restart freeze practical parallel algorithms are given

the complexity of acyclic conjunctive queries this paper deals with the evaluation of acyclic booleanconjunctive queries in relational databases by well known resultsof yannakakis 1981 this problem is solvable in polynomial time its precise complexity however has not been pinpointed so far weshow that the problem of evaluating acyclic boolean conjunctivequeries is complete for logcfl the class of decision problems thatare logspace reducible to a context free language since logcfl iscontained in ac1 and nc2 the evaluation problem of acyclic booleanconjunctive queries is highly parallelizable we present a paralleldatabase algorithm solving this problem with alogarithmic number ofparallel join operations the algorithm is generalized to computingthe output of relevant classes of non boolean queries we also showthat the acyclic versions of the following well known database andai problems are all logcfl complete the query output tuple problemfor conjunctive queries conjunctive query containment clausesubsumption and constraint satisfaction the logcfl completenessresult is extended to the class of queries of bounded tree widthand to other relevant query classes which are more general than theacyclic queries

a taxonomy of problems with fast parallel algorithms the class nc consists of problems solvable very fast in time polynomial in log n in parallel with a feasible polynomial number of processors many natural problems in nc are known in this paper an attempt is made to identify important subclasses of nc and give interesting examples in each subclass the notion of nc 1 reducibility is introduced and used throughout problem r is nc 1 reducible to problem s if r can be solved with uniform log depth circuits using oracles for s problems complete with respect to this reducibility are given for many of the subclasses of nc a general technique the parallel greedy algorithm is identified and used to show that finding a minimum spanning forest of a graph is reducible to the graph accessibility problem and hence is in nc 2 solvable by uniform boolean circuits of depth o log 2 n and polynomial size the class logcfl is given a new characterization in terms of circuit families the class det of problems reducible to integer determinants is defined and many examples given a new problem complete for deterministic polynomial time is given namely finding the lexicographically first maximal clique in a graph this paper is a revised version of s a cook 1983 in proceedings 1983 intl found comut sci conf lecture notes in computer science vol 158 pp 78 93 springer verlag berlin new york

finite element analysis of dynamic response of wrinkling membranes a new iterative scheme for finite element analysis of wrinkling membranes originally devised for static analysis is extended for analyzing dynamic response of wrinkling membranes the scheme is found to be successfully implemented with an explicit total lagrangian finite element code based upon the central difference method the finite element implementation of the scheme is straightforward and only minor modifications are needed for existing membrane finite element codes in light of application for contact impact discussed are a couple of existing contact algorithms which are well suited for treating contact impact of wrinkling membranes with rigid bodies the validity of the scheme is demonstrated via a numerical simulation of an inflating automotive airbag made of orthotropic membranes under impulse pressure loading

word problems and membership problems on compressed words we consider a compressed form of the word problem for finitely presented monoids where the input consists of two compressed representations of words over the generators of a monoid m and we ask whether these two words represent the same monoid element of m words are compressed using straight line programs i e context free grammars that generate exactly one word for several classes of finitely presented monoids we obtain completeness results for complexity classes in the range from p to expspace as a by product of our results on compressed word problems we obtain a fixed deterministic context free language with a pspace complete compressed membership problem the existence of such a language was open so far finally we will investigate the complexity of the compressed membership problem for various circuit complexity classes

the maximum flow problem is log space complete for p the space complexity of the maximum flow problem is investigated it is shown that the problem is log space complete for deterministic polynomial time thus the maximum flow problem probably has no algorithm which needs only o logk n storage space for any constant k another consequence is that there is probably no fast parallel algorithm for the maximum flow problem

tight complexity bounds for term matching problems abstract in this paper we study the sequential and parallel complexity of various important term matching problems these problems occur frequently in applications such as term rewriting functional programming and logic programming first we obtain non trivial lower bounds on the parallel complexity of the uninterpreted term matching problem we also establish the tightness of these bounds for some representations and several models we then characterize completely the sequential complexity of associative and commutative matching when the number of occurrences of variables is varied specifically we show that even if each variable is restricted to at most two occurrences in the terms both associative matching and commutative matching are np complete interestingly for the important restriction of boolean terms we show that commutative matching is np complete whereas associative matching has a linear time sequential algorithm for linear terms we significantly improve the existing upper bound for associative commutative matching and present a new algorithm for associative matching designing direct parallel algorithms for associative commutative matching of linear terms appears to be a difficult task despite this we have been able to resolve questions about the parallel complexity of these problems using complexity theoretic techniques finally an interesting consequence of the research reported here is the demonstration of a tighter relationship between associative commutative matching for linear terms and bipartite matching on both sequential and parallel models

parallel matrix and graph algorithms matrix multiplication algorithms for cube connected and perfect shuffle computers are presented it is shown that in both these models two n times n matrices can be multiplied in o n m log m time when n 2 m 1 leqq m leqq n processing elements pes are available when only m 2 1 leqq m leqq n pes are available two n times n matrices can be multiplied in o n 2 m m n m 2 61 time it is shown that many graph problems can be solved efficiently using the matrix multiplication algorithms

parallel construction of perfect matchings and hamiltonian cycles on dense graphs the intensive study of fast parallel and distributed algorithms for various routing and communications problems on graphs with good expanding properties ref pu1 ref pu2 ref ss is being carried out recently the parallel solutions for expanders that already exist ref pu 2 required an extensive randomization and an application of a randomized subroutine for the maximum matching problem in this paper we attack the problem of fast parallel algorithms for constructing perfect matchings and hamiltonian cycles on dense graph networks undirected graphs of minimal degree v over 2 somewhat surprisingly we design fast deterministic parallel algorithms for constructing both the perfect matchings and the hamiltonian cycles on the dense graphs the algorithm for constructing perfect matchings on dense graphs works in o log 2 n parallel time and o n 8 processors or o log 4 n parallel time and o n 4 processors on a crew pram the algorithm for constructing hamiltonian cycles on dense graphs works in o log 5 n parallel time and o n 4 processors on a crew pram our method of the parallel solution involves a development of new dense graph combinatorics suitable for fast parallelization

multiplication division and shift instructions in parallel random access machines abstract we prove that polynomial time on a parallel random access machine pram with unit cost multiplication and division or on a pram with unit cost shifts is equivalent to polynomial space on a turing machine pspace this extends the result that polynomial time on a basic pram is equivalent to pspace to hold when the pram is allowed multiplication or division or unrestricted shifts it also extends to the pram the results that polynomial time on a random access machine ram with multiplication is equivalent to pspace and that polynomial time on a ram with shifts that is a vector machine is equivalent to pspace we obtain simulations of uniform circuits by rams with enhanced instruction sets and use the enhanced rams to simulate prams with enhanced instruction sets

fast parallel computation of polynomials using few processors it is shown that any multivariate polynomial of degree d that can be computed sequentially in c steps can be computed in parallel in o log d log c log d steps using only cd o 1 processors

highly parallel computations modulo a number having only small prime factors abstract highly parallel algorithms computing the inverse discrete roots or a large power modulo a number that has only small prime factors are presented the elaborated uniform families of boolean circuits simultaneously achieve depth o log n and size o n0 1 for p uniformity and depth o log n log log n and size o n0 1 for log space uniformity

amplifying lower bounds by means of self reducibility we observe that many important computational problems in nc1 share a simple self reducibility property we then show that for any problem a having this self reducibility property a has polynomial size tc0 circuits if and only if it has tc0 circuits of size n1 for every 0 counting the number of wires in a circuit as the size of the circuit as an example of what this observation yields consider the boolean formula evaluation problem bfe which is complete for nc1 and has the self reducibility property it follows from a lower bound of impagliazzo paturi and saks that bfe requires depth d tc0 circuits of size n1 d if one were able to improve this lower bound to show that there is some constant 0 independent of the depth d such that every tc0 circuit family recognizing bfe has size at least n1 then it would follow that tc0 nc1 we show that proving lower bounds of the form n1 is not ruled out by the natural proof framework of razborov and rudich and hence there is currently no known barrier for separating classes such as acc0 tc0 and nc1 via existing natural approaches to proving circuit lower bounds we also show that problems with small uniform constant depth circuits have algorithms that simultaneously have small space and time bounds we then make use of known time space tradeoff lower bounds to show that sat requires uniform depth d tc0 and ac0 6 circuits of size n1 c for some constant c depending on d