Wojciech Plandowski - Academia.edu (original) (raw)

Papers by Wojciech Plandowski

Proceedings of the twenty-seventh annual ACM symposium on Theory of computing - STOC '95, 1995

... In most cases work-opt, irnality means ei-ther linear work or O(n log n ) work because no hig... more ... In most cases work-opt, irnality means ei-ther linear work or O(n log n ) work because no higher lower bounds are known. We call a work-optimal algor-ithm w(~rk-tirlle-o~~tirllal or wt-op tim al if in addition its * Heiuz Nixdorf hstitute, LJniversity of F'aderboru, 11-3:3095 ...

The power of weighted finite automata to describe very complex images was widely studied, see [5,... more The power of weighted finite automata to describe very complex images was widely studied, see [5, 6, 7]. Finite automata can be also used as an effective tool for compression of two-dimensional images. There are some software packages using this type of compression, see [12, 6]. We consider the complexity of some pattern-matching problems for two-dimensional images which are highly

Lecture Notes in Computer Science, 1998

One of the most intricate algorithms related to words is Makanin's algorithm solving... more One of the most intricate algorithms related to words is Makanin's algorithm solvingword equations. The algorithm is very complicated and the complexity of the problemof solving word equations is not well understood. Word equations can be used todefine various properties of strings, e.g. general versions of pattern-matching withvariables. This paper is devoted to introduce a new approach and to study relationsbetween Lempel-Ziv compressions and word equations. Instead of dealing with very...

Theoretical Computer Science, 2003

We formulate and prove a defect theorem for bi-inÿnite words. Let X be a ÿnite set of words over ... more We formulate and prove a defect theorem for bi-inÿnite words. Let X be a ÿnite set of words over a ÿnite alphabet. If a nonperiodic bi-inÿnite word w has two X -factorizations, then the combinatorial rank of X is at most card(X ) − 1, i.e., there exists a set F such that X ⊆ F + with card(F) ¡ card(X ). Moreover, in the case when the combinatorial rank of X equals card(X ), the number of periodic bi-inÿnite words which have two di erent X -factorizations is ÿnite.

Denote by LZ(w) the coded form of a string w produced by Lempel-Ziv encoding algorithm. We consid... more Denote by LZ(w) the coded form of a string w produced by Lempel-Ziv encoding algorithm. We consider several classical algorithmic problems for texts in the compressed setting. The rst of them is the equality-testing: given LZ(w) and integers i; j; k test the equality: w i: : : i + k] = w j : : : j + k]. We give a simple and e cient randomized algorithm for this problem using the nger-printing idea. The equality testing is reduced to the equivalence of certain context-free grammars generating single strings. The equality-testing is the bottleneck in other algorithms for compressed texts. We relate the time complexity of several classical problems for texts to the complexity Eq(n) of equality-testing. Assume n = jLZ (T)j, m = jLZ (P)j and U = jT j. Then we can compute the compressed representations of the sets of occurrences of P in T, periods of T, palindromes of T, and squares of T respectively in times O(n log 2 U Eq(m) + n 2 log U), O(n log 2 U Eq(n) + n 2 log U), O(n log 2 U Eq(n)+n 2 log U) and O(n 2 log 3 U Eq(n)+n 3 log 2 U), where Eq(n) = O(n log log n). The randomization improves considerably upon the known deterministic algorithms ( 7] and 8]).

ABSTRACT We show a simple O(n log n) time algorithm computing the order of repetition in a string... more ABSTRACT We show a simple O(n log n) time algorithm computing the order of repetition in a string. A parallel version of the algorithm works in O(log

We consider a version of pattern matching useful in processing large musical data: δ-matching, wh... more We consider a version of pattern matching useful in processing large musical data: δ-matching, which consists in finding matches which are δ-approximate in the sense of the distance measured as maximum difference between symbols. The alphabet is an interval of integers, and the distance between two symbols a, b is measured as |a - b|. We present δ-matching algorithms fast

Combinatorial Pattern Matching, 2002

Abstract: We consider a version of pattern matching useful in processing large musical data: delt... more Abstract: We consider a version of pattern matching useful in processing large musical data: delta-matching, which consists in finding matches which are delta-approximate in the sense of the distance measured as maximum difference between symbols. The alphabet is an interval of integers, and the distance between two symbols a, b is measured as |a - b|. We present delta-matching algorithms

... Warszawa, {lechu, wojt ekpl, rytter}~ailuv, edu. pl Abstract. A new string-matching algorithm... more ... Warszawa, {lechu, wojt ekpl, rytter}~ailuv, edu. pl Abstract. A new string-matching algorithm working in constant space and linear time is presented. It is based on a powerful idea of sampling, originally introduced in parallel computations. The algorithm uses a sam-ple S which ...

Lecture Notes in Computer Science, 1995

We present the rst known (alphabet independent) algorithm for two-dimensional pattern matching wh... more We present the rst known (alphabet independent) algorithm for two-dimensional pattern matching which works in linear time and small space simultaneously. The searching phase of our algorithm works in O(1) space and is followed by pattern preprocessing performed in O(log m) space. Up to now there was not known even any e cient sublinear space algorithm for this problem. The main tools in our algorithm are several 2-dimensional variations of deterministic sampling, originally used in parallel pattern matching: small, frame and wide samples. Another novel idea used in our algorithm is the technique of zooming sequences: the sequences of nonperiodic decreasing parts of the pattern (samples) of similar regular shapes. Their regularity allows to encode the zooming sequences in small memory (logarithmic number of bits) while nonperiodicity allows to make shifts (kill positions as candidates for a match) in a way amortizing the work. The preprocessing phase is recursive, its structure is similar to the linear time algorithm for the selection problem. The stack of the recursion consists of logarithmic number of integers. Our algorithm is rather complicated, but all known alphabetindependent linear time algorithms (even with unrestricted space) for 2d-matching are quite complicated, too.

Lecture Notes in Computer Science, 1998

We prove the following two variants of the defect theorem. Let X be a finiteset of words over a f... more We prove the following two variants of the defect theorem. Let X be a finiteset of words over a finite alphabet. Then if a nonperiodic bi-infiniteword w has two X-factorizations, then the combinatorial rank of X isat most card(X) \Gamma 1, i.e. there exists a set F such that X ` F

We consider several basic problems for texts and show that if the input texts are given by their ... more We consider several basic problems for texts and show that if the input texts are given by their Lempel-Ziv codes then the problems can be solved deterministically in polynomial time in the case when the original (uncompressed) texts are of exponential size. The growing importance of massively stored information requires new approaches to algorithms for compressed texts without decompressing. Denote by LZ(ω) the version of a string ω produced by Lempel-Ziv encoding algorithm. For given compressed strings LZ(T), LZ(P) we give the first known deterministic polynomial time algorithms to compute compressed representations of the set of all occurrences of the patternP in T, all periods of T, all palindromes of T, and all squares of T. Then we consider several classical language recognition problems:

Combinatorial Pattern Matching, 1999

... 1. A. Amir and G. Benson, Efficient two dimensional compressed matching, Proc. of the 2nd IEE... more ... 1. A. Amir and G. Benson, Efficient two dimensional compressed matching, Proc. of the 2nd IEEE Data Compression Conference 279-288 (1992). 2. P. Berman, M. Karpinski, L. Larmore, W. Plandowski, W. Rytter, The compexity of pattern matching of highly compressed two ...

… Computer Science in Honor of Arto …, 1999

... 3. A. Amir, G. Benson, and M. Farach, Optimal two-dimensional compressed matching, Proc. ... ... more ... 3. A. Amir, G. Benson, and M. Farach, Optimal two-dimensional compressed matching, Proc. ... Z. Galil, Optimal parallel algorithms for periods, palindromes and squares, in ICALP'92, 296-307 5. P. Berman, M. Karpi nski, L. Larmore, W. Plandowski, and W. Rytter, The complexity ...

Nordic Journal of Computing, 2000

... 9. Samuel Eilenberg, Automata, Languages, and Machines, Academic Press, Inc., Orlando, FL, 19... more ... 9. Samuel Eilenberg, Automata, Languages, and Machines, Academic Press, Inc., Orlando, FL, 1974. 10. ... 11. Leszek Gasieniec , Marek Karpinski , Wojciech Plandowski , Wojciech Rytter, Efficient Algorithms for Lempel-Zip Encoding (Extended Abstract), Proceedings of the 5th ...

Proceedings of the twenty-seventh annual ACM symposium on Theory of computing - STOC '95, 1995

... In most cases work-opt, irnality means ei-ther linear work or O(n log n ) work because no hig... more ... In most cases work-opt, irnality means ei-ther linear work or O(n log n ) work because no higher lower bounds are known. We call a work-optimal algor-ithm w(~rk-tirlle-o~~tirllal or wt-op tim al if in addition its * Heiuz Nixdorf hstitute, LJniversity of F'aderboru, 11-3:3095 ...

The power of weighted finite automata to describe very complex images was widely studied, see [5,... more The power of weighted finite automata to describe very complex images was widely studied, see [5, 6, 7]. Finite automata can be also used as an effective tool for compression of two-dimensional images. There are some software packages using this type of compression, see [12, 6]. We consider the complexity of some pattern-matching problems for two-dimensional images which are highly

Lecture Notes in Computer Science, 1998

One of the most intricate algorithms related to words is Makanin's algorithm solving... more One of the most intricate algorithms related to words is Makanin's algorithm solvingword equations. The algorithm is very complicated and the complexity of the problemof solving word equations is not well understood. Word equations can be used todefine various properties of strings, e.g. general versions of pattern-matching withvariables. This paper is devoted to introduce a new approach and to study relationsbetween Lempel-Ziv compressions and word equations. Instead of dealing with very...

Theoretical Computer Science, 2003

We formulate and prove a defect theorem for bi-inÿnite words. Let X be a ÿnite set of words over ... more We formulate and prove a defect theorem for bi-inÿnite words. Let X be a ÿnite set of words over a ÿnite alphabet. If a nonperiodic bi-inÿnite word w has two X -factorizations, then the combinatorial rank of X is at most card(X ) − 1, i.e., there exists a set F such that X ⊆ F + with card(F) ¡ card(X ). Moreover, in the case when the combinatorial rank of X equals card(X ), the number of periodic bi-inÿnite words which have two di erent X -factorizations is ÿnite.

Denote by LZ(w) the coded form of a string w produced by Lempel-Ziv encoding algorithm. We consid... more Denote by LZ(w) the coded form of a string w produced by Lempel-Ziv encoding algorithm. We consider several classical algorithmic problems for texts in the compressed setting. The rst of them is the equality-testing: given LZ(w) and integers i; j; k test the equality: w i: : : i + k] = w j : : : j + k]. We give a simple and e cient randomized algorithm for this problem using the nger-printing idea. The equality testing is reduced to the equivalence of certain context-free grammars generating single strings. The equality-testing is the bottleneck in other algorithms for compressed texts. We relate the time complexity of several classical problems for texts to the complexity Eq(n) of equality-testing. Assume n = jLZ (T)j, m = jLZ (P)j and U = jT j. Then we can compute the compressed representations of the sets of occurrences of P in T, periods of T, palindromes of T, and squares of T respectively in times O(n log 2 U Eq(m) + n 2 log U), O(n log 2 U Eq(n) + n 2 log U), O(n log 2 U Eq(n)+n 2 log U) and O(n 2 log 3 U Eq(n)+n 3 log 2 U), where Eq(n) = O(n log log n). The randomization improves considerably upon the known deterministic algorithms ( 7] and 8]).

ABSTRACT We show a simple O(n log n) time algorithm computing the order of repetition in a string... more ABSTRACT We show a simple O(n log n) time algorithm computing the order of repetition in a string. A parallel version of the algorithm works in O(log

We consider a version of pattern matching useful in processing large musical data: δ-matching, wh... more We consider a version of pattern matching useful in processing large musical data: δ-matching, which consists in finding matches which are δ-approximate in the sense of the distance measured as maximum difference between symbols. The alphabet is an interval of integers, and the distance between two symbols a, b is measured as |a - b|. We present δ-matching algorithms fast

Combinatorial Pattern Matching, 2002

Abstract: We consider a version of pattern matching useful in processing large musical data: delt... more Abstract: We consider a version of pattern matching useful in processing large musical data: delta-matching, which consists in finding matches which are delta-approximate in the sense of the distance measured as maximum difference between symbols. The alphabet is an interval of integers, and the distance between two symbols a, b is measured as |a - b|. We present delta-matching algorithms

... Warszawa, {lechu, wojt ekpl, rytter}~ailuv, edu. pl Abstract. A new string-matching algorithm... more ... Warszawa, {lechu, wojt ekpl, rytter}~ailuv, edu. pl Abstract. A new string-matching algorithm working in constant space and linear time is presented. It is based on a powerful idea of sampling, originally introduced in parallel computations. The algorithm uses a sam-ple S which ...

Lecture Notes in Computer Science, 1995

We present the rst known (alphabet independent) algorithm for two-dimensional pattern matching wh... more We present the rst known (alphabet independent) algorithm for two-dimensional pattern matching which works in linear time and small space simultaneously. The searching phase of our algorithm works in O(1) space and is followed by pattern preprocessing performed in O(log m) space. Up to now there was not known even any e cient sublinear space algorithm for this problem. The main tools in our algorithm are several 2-dimensional variations of deterministic sampling, originally used in parallel pattern matching: small, frame and wide samples. Another novel idea used in our algorithm is the technique of zooming sequences: the sequences of nonperiodic decreasing parts of the pattern (samples) of similar regular shapes. Their regularity allows to encode the zooming sequences in small memory (logarithmic number of bits) while nonperiodicity allows to make shifts (kill positions as candidates for a match) in a way amortizing the work. The preprocessing phase is recursive, its structure is similar to the linear time algorithm for the selection problem. The stack of the recursion consists of logarithmic number of integers. Our algorithm is rather complicated, but all known alphabetindependent linear time algorithms (even with unrestricted space) for 2d-matching are quite complicated, too.

Lecture Notes in Computer Science, 1998

We prove the following two variants of the defect theorem. Let X be a finiteset of words over a f... more We prove the following two variants of the defect theorem. Let X be a finiteset of words over a finite alphabet. Then if a nonperiodic bi-infiniteword w has two X-factorizations, then the combinatorial rank of X isat most card(X) \Gamma 1, i.e. there exists a set F such that X ` F

We consider several basic problems for texts and show that if the input texts are given by their ... more We consider several basic problems for texts and show that if the input texts are given by their Lempel-Ziv codes then the problems can be solved deterministically in polynomial time in the case when the original (uncompressed) texts are of exponential size. The growing importance of massively stored information requires new approaches to algorithms for compressed texts without decompressing. Denote by LZ(ω) the version of a string ω produced by Lempel-Ziv encoding algorithm. For given compressed strings LZ(T), LZ(P) we give the first known deterministic polynomial time algorithms to compute compressed representations of the set of all occurrences of the patternP in T, all periods of T, all palindromes of T, and all squares of T. Then we consider several classical language recognition problems:

Combinatorial Pattern Matching, 1999

... 1. A. Amir and G. Benson, Efficient two dimensional compressed matching, Proc. of the 2nd IEE... more ... 1. A. Amir and G. Benson, Efficient two dimensional compressed matching, Proc. of the 2nd IEEE Data Compression Conference 279-288 (1992). 2. P. Berman, M. Karpinski, L. Larmore, W. Plandowski, W. Rytter, The compexity of pattern matching of highly compressed two ...

… Computer Science in Honor of Arto …, 1999

... 3. A. Amir, G. Benson, and M. Farach, Optimal two-dimensional compressed matching, Proc. ... ... more ... 3. A. Amir, G. Benson, and M. Farach, Optimal two-dimensional compressed matching, Proc. ... Z. Galil, Optimal parallel algorithms for periods, palindromes and squares, in ICALP'92, 296-307 5. P. Berman, M. Karpi nski, L. Larmore, W. Plandowski, and W. Rytter, The complexity ...

Nordic Journal of Computing, 2000

... 9. Samuel Eilenberg, Automata, Languages, and Machines, Academic Press, Inc., Orlando, FL, 19... more ... 9. Samuel Eilenberg, Automata, Languages, and Machines, Academic Press, Inc., Orlando, FL, 1974. 10. ... 11. Leszek Gasieniec , Marek Karpinski , Wojciech Plandowski , Wojciech Rytter, Efficient Algorithms for Lempel-Zip Encoding (Extended Abstract), Proceedings of the 5th ...