Section: Διαλέξεις | Algorithms and Complexity

Calendar

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21 October 2026, 10:47 PM
Αριστείδης Παγουρτζής
Ανάρτηση 1ης σειράς γραπτών ασκήσεων

Section outline

Διάλεξη 28/9/2026 : Εισαγωγή και διαδικαστικά. Εισαγωγικές έννοιες, προβλήματα απόφασης, και βελτιστοποίησης, εύρεσης και καταμέτρησης.

Διάλεξη 1/10/2026 : Εκτίμηση πολυπλοκότητας, ασυμπτωτικός συμβολισμός.

Διάλεξη 5/10/2026 : Ασυμπτωτικός συμβολισμός (σύντομη επανάληψη, παραδείγματα). Το πρόβλημα union-find. Union by rank. Path compression.

Διάλεξη 8/10/2026 : Απόδειξη Hopcroft - Ulmann για πολυπλοκότητα Ο(mlog*n) για m finds και n unions. ADT Λεξικού. Hash tables. Cuckoo hashing. Bloom filters.

Διάλεξη 12/10/2026 : Εμβάθυνση σε hash functions. Universal hash families. Δείτε σχετικές διαφάνειες του Uri Zwick.

Διάλεξη 15/10/2026: Hashing με open addressing: απόδειξη του παράγοντα φόρτου για uniform probing, γραμμική και τετραγωνική διερεύνηση, διπλός κατακερματισμός. Ουρές προτεραιότητας, σωροί: εισαγωγή, διαγραφή, γραμμική κατασκευή σωρού.

Διάλεξη 19/10/2026: Σωροί: σύντομη επανάληψη και Heapsort. Η μέθοδος Διαίρει και Βασίλευε (Divide and Conquer): Mergesort και Master Theorem.

Διάλεξη 22/10/2026: Master Theorem (σύντομη επανάληψη). Αλγόριθμοι Divide and Conquer: πολλ/σμός ακεραίων, ύψωση σε δύναμη, πολλ/σμός πινάκων, αριθμοί Fibonacci. Μέτρηση αντιστροφών (πρώτη προσέγγιση, σε Ο(nlog²n).

October 2026

Section outline