Exact Distance Oracles for Planar Graphs with Failing Vertices

We consider exact distance oracles for directed weighted planar graphs in the presence of failing vertices. Given a source vertex $u$, a target vertex $v$ and a set $X$ of $k$ failed vertices, such an oracle returns the length of a shortest $u$-to-$v$ path that avoids all vertices in $X$. We propose oracles that can handle any number $k$ of failures. More specifically, for a directed weighted planar graph with $n$ vertices, any constant $k$, and for any $q \in [1,\sqrt n]$, we propose an oracle of size $\tilde{\mathcal{O}}(\frac{n^{k+3/2}}{q^{2k+1}})$ that answers queries in $\tilde{\mathcal{O}}(q)$ time. In particular, we show an $\tilde{\mathcal{O}}(n)$-size, $\tilde{\mathcal{O}}(\sqrt{n})$-query-time oracle for any constant $k$. This matches, up to polylogarithmic factors, the fastest failure-free distance oracles with nearly linear space. For single vertex failures ($k=1$), our $\tilde{\mathcal{O}}(\frac{n^{5/2}}{q^3})$-size, $\tilde{\mathcal{O}}(q)$-query-time oracle improves over the previously best known tradeoff of Baswana et al. [SODA 2012] by polynomial factors for $q = \Omega(n^t)$, $t \in (1/4,1/2]$. For multiple failures, no planarity exploiting results were previously known

Repetition Detection in a Dynamic String

A string UU for a non-empty string U is called a square. Squares have been well-studied both from a combinatorial and an algorithmic perspective. In this paper, we are the first to consider the problem of maintaining a representation of the squares in a dynamic string S of length at most n. We present an algorithm that updates this representation in n^o(1) time. This representation allows us to report a longest square-substring of S in O(1) time and all square-substrings of S in O(output) time. We achieve this by introducing a novel tool - maintaining prefix-suffix matches of two dynamic strings. We extend the above result to address the problem of maintaining a representation of all runs (maximal repetitions) of the string. Runs are known to capture the periodic structure of a string, and, as an application, we show that our representation of runs allows us to efficiently answer periodicity queries for substrings of a dynamic string. These queries have proven useful in static pattern matching problems and our techniques have the potential of offering solutions to these problems in a dynamic text setting

Faster Approximate Pattern Matching: A Unified Approach

Approximate pattern matching is a natural and well-studied problem on strings: Given a text $T$, a pattern $P$, and a threshold $k$, find (the starting positions of) all substrings of $T$ that are at distance at most $k$ from $P$. We consider the two most fundamental string metrics: the Hamming distance and the edit distance. Under the Hamming distance, we search for substrings of $T$ that have at most $k$ mismatches with $P$, while under the edit distance, we search for substrings of $T$ that can be transformed to $P$ with at most $k$ edits. Exact occurrences of $P$ in $T$ have a very simple structure: If we assume for simplicity that $|T| \le 3|P|/2$ and trim $T$ so that $P$ occurs both as a prefix and as a suffix of $T$, then both $P$ and $T$ are periodic with a common period. However, an analogous characterization for the structure of occurrences with up to $k$ mismatches was proved only recently by Bringmann et al. [SODA'19]: Either there are $O(k^2)$ $k$-mismatch occurrences of $P$ in $T$, or both $P$ and $T$ are at Hamming distance $O(k)$ from strings with a common period $O(m/k)$. We tighten this characterization by showing that there are $O(k)$ $k$-mismatch occurrences in the case when the pattern is not (approximately) periodic, and we lift it to the edit distance setting, where we tightly bound the number of $k$-edit occurrences by $O(k^2)$ in the non-periodic case. Our proofs are constructive and let us obtain a unified framework for approximate pattern matching for both considered distances. We showcase the generality of our framework with results for the fully-compressed setting (where $T$ and $P$ are given as a straight-line program) and for the dynamic setting (where we extend a data structure of Gawrychowski et al. [SODA'18]).Comment: 74 pages, 7 figures, FOCS'2

Dynamic Longest Common Substring in Polylogarithmic Time

The longest common substring problem consists in finding a longest string that appears as a (contiguous) substring of two input strings. We consider the dynamic variant of this problem, in which we are to maintain two dynamic strings S and T, each of length at most n, that undergo substitutions of letters, in order to be able to return a longest common substring after each substitution. Recently, Amir et al. [ESA 2019] presented a solution for this problem that needs only ??(n^(2/3)) time per update. This brought the challenge of determining whether there exists a faster solution with polylogarithmic update time, or (as is the case for other dynamic problems), we should expect a polynomial (conditional) lower bound. We answer this question by designing a significantly faster algorithm that processes each substitution in amortized log^?(1) n time with high probability. Our solution relies on exploiting the local consistency of the parsing of a collection of dynamic strings due to Gawrychowski et al. [SODA 2018], and on maintaining two dynamic trees with labeled bicolored leaves, so that after each update we can report a pair of nodes, one from each tree, of maximum combined weight, which have at least one common leaf-descendant of each color. We complement this with a lower bound of ?(log n/ log log n) for the update time of any polynomial-size data structure that maintains the LCS of two dynamic strings, even allowing amortization and randomization

Λιποσωμιακή βουπιβακαϊνη. Φαρμακολογικές ιδιότητες και κλινικές εφαρμογές

Σκοπός: Σκοπός αυτής της εργασίας είναι να συνοψίσει τα μέχρι σήμερα δημοσιευμένα δεδομένα από τη χρήση της λιποσωμιακής βουπιβακαΐνης. Η αντιμετώπιση του οξέος μετεγχειρητικού πόνου είναι κεφαλαιώδους σημασίας για την αποφυγή μετεγχειρητικών επιπλοκών και τη μείωση της διάρκειας και του κόστους νοσηλείας. Στα πλαίσια αυτά κερδίζει συνεχώς έδαφος η πολυπαραγοντική αναλγησία μέρος της οποίας είναι και η χρήση τοπικών αναισθητικών. Η λιποσωμιακή βουπιβακαΐνη αποτελεί μια νέα μορφή τοπικού αναισθητικού που υπόσχεται διάρκεια δράσης που μπορεί να ξεπεράσει τις 48 ώρες. Στην εργασία αυτή θα γίνει προσπάθεια να αναλυθούν οι εγκεκριμένοι τρόποι χρήσης της λιποσωμιακής βουπιβακαΐνης, η διάρκεια δράσης που επιτυγχάνεται με κάθε τρόπο εφαρμογής, η υπεροχή ή όχι έναντι ενεργού παράγοντα σύγκρισης ή εικονικού φαρμάκου, οι ανεπιθύμητες ενέργειες που παρουσιάστηκαν κατά τη χρήση της καθώς και εφαρμογές που βρίσκονται ακόμη στο στάδιο της πειραματικής διερεύνησης προκειμένου να διευρυνθούν οι ενδείξεις χρήσης του φαρμάκου. Συμπεράσματα: Η λιποσωμιακή βουπιβακαΐνη έχει λάβει μέχρι σήμερα έγκριση χρήσης μόνο στις Ηνωμένες Πολιτείες Αμερικής για διήθηση χειρουργικού τραύματος και για πραγματοποίηση περιφερικών νευρικών αποκλεισμών μόνο για αποκλεισμό στο επίπεδο του εγκάρσιου κοιλιακού μυός (Transversus Abdominis Plane block, TAP block) και αποκλεισμό βραχιονίου πλέγματος με διασκαληνική προσπέλαση μόνο για μετεγχειρητική αναλγησία. Παρά τον αρχικό ενθουσιασμό, νεότερες μελέτες δεν συνηγορούν υπέρ της χρήσης της λιποσωμιακής βουπιβακαΐνης για διήθηση χειρουργικού τραύματος καθώς δε φαίνεται να προσφέρει αναλγησία που να ξεπερνά τις 24 ώρες. Όσον αφορά τους περιφερικούς νευρικούς αποκλεισμούς, οι μελέτες, παρ’ ότι σχετικά λίγες, είναι ενθαρρυντικές, καθώς φαίνεται η διάρκεια δράσης της λιποσωμιακής βουπιβακαΐνης να ξεπερνά τις 48 ώρες. Όσον αφορά το προφίλ ασφαλείας, η χρήση της λιποσωμιακής βουπιβακαΐνης σε όλες τις μελέτες αποδείχτηκε ασφαλής και καλά ανεκτή.Objective: The object of the present study is to summarize the published data from the use of liposomal bupivacaine until now. The treatment of acute postoperative pain is of major importance to avoid postoperative complications, shorten the length of hospital stay and reduce hospitalization cost. In favor of these, a multimodal approach is gaining popularity, part of which is the use of regional anesthetic agents. Liposomal bupivacaine is a new drug formulation that promises duration of action beyond 48 hours. This study will attempt to analyze the approved applications of the drug, the duration of action that can be achieved with every application, the superiority against comparison with active compound or placebo, the adverse events that were reported during its use and to explore applications that are not yet approved but are in clinical trial to extend the indications of use. Conclusions: Liposomal bupivacaine is approved, to date, only in the United States of America for use in infiltration of surgical site and to perform peripheral nerve blocks only for Transversus Abdominis Plane block (TAP block) and brachial plexus block, interscalene approach, for postoperative analgesia exclusively. Despite early enthusiasm, newer studies do not favor the use of liposomal bupivacaine for surgical site infiltration because it seems that it cannot offer analgesia beyond 24 hours. For peripheral nerve blocks, the studies, despite their relatively small number, are encouraging as it seems that the duration of action of liposomal bupivacaine extends over 48 hours. Regarding the safety profile, the use of liposomal bupivacaine was deemed safe and well tolerated in all the studies

An Almost Optimal Edit Distance Oracle

We consider the problem of preprocessing two strings S and T, of lengths m and n, respectively, in order to be able to efficiently answer the following queries: Given positions i,j in S and positions a,b in T, return the optimal alignment score of S[i..j] and T[a..b]. Let N = mn. We present an oracle with preprocessing time N^{1+o(1)} and space N^{1+o(1)} that answers queries in log^{2+o(1)}N time. In other words, we show that we can efficiently query for the alignment score of every pair of substrings after preprocessing the input for almost the same time it takes to compute just the alignment of S and T. Our oracle uses ideas from our distance oracle for planar graphs [STOC 2019] and exploits the special structure of the alignment graph. Conditioned on popular hardness conjectures, this result is optimal up to subpolynomial factors. Our results apply to both edit distance and longest common subsequence (LCS). The best previously known oracle with construction time and size ?(N) has slow ?(?N) query time [Sakai, TCS 2019], and the one with size N^{1+o(1)} and query time log^{2+o(1)}N (using a planar graph distance oracle) has slow ?(N^{3/2}) construction time [Long & Pettie, SODA 2021]. We improve both approaches by roughly a ? N factor

Double Bass Accompaniment and Technological Innovation in Jazz Music

Η παρούσα διπλωματική εργασία πραγματεύεται το ρόλο του κοντραμπάσου ως όργανο συνοδείας στη Jazz μουσική. Τα 3 κύρια κεφάλαια της εργασίας καλύπτουν α) ενδελεχή ιστορική αναδρομή και απεικόνιση του εξελισσόμενου ρόλου, β) πώς τα τεχνολογικά μέσα επέδρασαν σε αυτή την εξέλιξη και γ) προοπτικές περαιτέρω εξέλιξης του ρόλου με χρήση νέων τεχνολογιώνThis dissertation deals with the role of the double bass as an accompanying instrument in Jazz music. The 3 main sections of the work cover a) a thorough historical background and depiction of the evolving role, b) how technology influenced this development and c) prospects for further development of the role using new technologie