Giuseppe F. Italiano

On the optimal placement of web proxies in the Internet

Web caching or web proxy has been considered as the prime vehicle of coping with the ever-increasing demand for information retrieval over the Internet, the WWW being a typical example. Existing work on web proxy has primarily focused on content based caching; relatively less attention has been given to the development of proper placement strategies for the potential web proxies in the Internet. In this paper, we argue that the placement of web proxies is critical to the performance and further investigates the optimal placement policy of web proxies for a target web server in the Internet. The objective is to optimize a given performance measure for the target web server subject to system resources and traffic pattern. Specifically, we are interested in finding the optimal placement of multiple web proxies (M) among potential sites (N) under a given traffic pattern. We show this can be modeled a dynamic programming problem. We further obtain the optimal solution for the tree topology using O(N/sup 3/M/sup 2/) time.

Sparsification—a technique for speeding up dynamic graph algorithms

We provide data strutures that maintain a graph as edges are inserted and deleted, and keep track of the following properties with the following times: minimum spanning forests, graph connectivity, graph 2-edge connectivity, and bipartiteness in time<italic>O</italic>(<italic>n</italic><supscrpt>1/2</supscrpt>) per change; 3-edge connectivity, in time <italic>O</italic>(<italic>n</italic><supscrpt>2/3</supscrpt>) per change; 4-edge connectivity, in time <italic>O</italic>(<italic>n</italic>α(<italic>n</italic>)) per change; <italic>k</italic>-edge connectivity for constant <italic>k</italic>, in time <italic>O</italic>(<italic>n</italic>log<italic>n</italic>) per change;2-vertex connectivity, and 3-vertex connectivity, in the <italic>O</italic>(<italic>n</italic>) per change; and 4-vertex connectivity, in time <italic>O</italic>(<italic>n</italic>α(<italic>n</italic>)) per change. Further results speed up the insertion times to match the bounds of known partially dynamic algorithms. All our algorithms are based on a new technique that transforms an algorithm for sparse graphs into one that will work on any graph, which we call <italic>sparsification.</italic>

Dynamic graph algorithms

In dynamic graph algorithms the following provide-or-boundproblem has to be solved quickly: Given a set S containing a subset R and a way of generating random elements fromS testing for membership inR, either (i) provide an element of R or (ii) give a (small) upper bound on the size of R that holds with high probability. We give an optimal algorithm for this problem. This algorithm improves the time per operation for various dyamic graph algorithms by a factor ofO(logn). For example, it improves the time per update for fully dynamic connectivity fromO(log n) toO(log n).

Sparse dynamic programming I: linear cost functions

Dynamic programming solutions to a number of different recurrence equations for sequence comparison and for RNA secondary structure prediction are considered. These recurrences are defined over a number of points that is quadratic in the input size; however only a sparse set matters for the result. Efficient algorithms for these problems are given, when the weight functions used in the recurrences are taken to be linear. The time complexity of the algorithms depends almost linearly on the number of points that need to be considered; when the problems are sparse this results in a substantial speed-up over known algorithms.

Data structures and algorithms for disjoint set union problems

This paper surveys algorithmic techniques and data structures that have been proposed tosolve thesetunion problem and its variants, Thediscovery of these data structures required anew set ofalgorithmic tools that have proved useful in other areas. Special attention is devoted to recent extensions of the original set union problem, and an attempt is made to provide a unifying theoretical framework for this growing body of algorithms.

Maintenance of a minimum spanning forest in a dynamic plane graph

Abstract : We give efficient algorithms for maintaining a minimum spanning forest of a planar graph subject to on-line modifications. The modifications supported include changes in the edge weights, and insertion and deletion of edges and vertices. To implement the algorithms, we develop a data structure called an edge-ordered dynamic tree, which is a variant of the dynamic tree data structure of Sleator and Tarjan. Using this data structure, our algorithms run in O(log n) time per operation and O(n) space. The algorithms can be used to maintain the connected components of a dynamic planar graph in O(log n) time per operation.

Algorithm engineering

Algorithm Engineering is concerned with the design, analysis, implementation, tuning, debugging and experimental evaluation of computer programs for solving algorithmic problems. It provides methodologies and tools for developing and engineering efficient algorithmic codes and aims at integrating and reinforcing traditional theoretical approaches for the design and analysis of algorithms and data structures.

New Algorithms for Examination Timetabling

In examination timetabling a given set of examinations must be assigned to as few time slots as possible so as to satisfy certain side constraints and so as to reduce penalties deriving from proximity constraints. In this paper, we present new algorithms for this problem and report the results of an extensive experimental study. All our algorithms are based on local search and are compared with other existing implementations in the literature.

Amortized efficiency of a path retrieval data structure

A data structure is presented for the problem of maintaining a digraph under an arbitrary sequence of two kinds of operations: an Add operation that inserts an arc in the digraph, and a Searchpath operation that checks the presence of a path between a pair of nodes. Our data structure supports both operations in O(n) amortized time and requires O(n2) space, where n is the number of nodes in the digraph.

Finding paths and deleting edges in directed acyclic graphs

Significant progress has recently been made in the design of efficient dynamic data structures for the representation of graphs. The data structures support the efficient insertion and/or deletion of edges in a graph, in addition to certain types of queries for the graph [2-5,7-15,17,18]. D_ynamic data structures of this nature are very useful for the on-line computation of graph properties and related problems. In particular, much attention has been devottj to the on-line computation of the connected components of graphs [4,5,7,8,10,11,13,14,15,17]. As far as undirected graphs are concerned, the algorithm proposed by Even and Shiloach [4] answers q questions about the existence of a path between two nodes while deleting an arbitrary number of edges in a graph with m edges and n nodes in 0( q + mn) time. A more general version of this problem has been discussed in [7], in which O(n) time for each insertion or deletion of edges was realized. Recently, Frederickson IS] improved this bound to O(G). In case of directed graphs, the on-line computation of the transitive closure was first tackled by Ibaraki and Katoh [8], who proposed an algorithm for maintaining the transitive closure of a digraph with n nodes and m edges in: * 0(n3) time for an arbitrary number of edge insertions, l O(n*(m + n)) time for an arbitrary number of edge deletions. In [lo], a data structure was introduced supporting both path retrieval operations and insertions of edges in O(n) amortized [16] time, thus improving the time required to maintain the transitive closure of a digraph during m edge insertions from 0(n3) to 0( mn). This data structure enables one not only to answer the question whether two nodes are connected in constant time but also to return a path between any couple of nodes in O(I) time, where I is the length of the achieved path. In this paper we restrict ourselves to directed acyclic graphs (DAGs), and show how to return an arbitrarily chosen path between couples of nodes (if it exists) during the deletion of edges in ark efficient manner. Thus, we are given a DAG G = (V, E) with n nodes and m edges and we want to perform on it a sequence of intermixed operations of the. following two hinds: