Showing papers by "Richard Cole published in 2003"

Pricing network edges for heterogeneous selfish users

Abstract: We study the negative consequences of selfish behavior in a congested network and economic means of influencing such behavior. We consider a model of selfish routing in which the latency experienced by network traffic on an edge of the network is a function of the edge congestion, and network users are assumed to selfishly route traffic on minimum-latency paths. The quality of a routing of traffic is measured by the sum of travel times (the total latency).It is well known that the outcome of selfish routing (a Nash equilibrium) does not minimize the total latency. An ancient strategy for improving the selfish solution is the principle of marginal cost pricing, which asserts that on each edge of the network, each network user on the edge should pay a tax offsetting the congestion effects caused by its presence. By pricing network edges according to this principle, the inefficiency of selfish routing can always be eradicated.This result, while fundamental, assumes a very strong homogeneity property: all network users are assumed to trade off time and money in an identical way. The guarantee also ignores both the algorithmic aspects of edge pricing and the unfortunate possibility that an efficient routing of traffic might only be achieved with exorbitant taxes. Motivated by these shortcomings, we extend this classical work on edge pricing in several different directions and prove the following results.We prove that the edges of a single-commodity network can always be priced so that an optimal routing of traffic arises as a Nash equilibrium, even for very general heterogeneous populations of network users.When there are only finitely many different types of network users and all edge latency functions are convex, we show how to compute such edge prices efficiently.We prove that an easy-to-check mathematical condition on the population of heterogeneous network users is both necessary and sufficient for the existence of edge prices that induce an optimal routing while requiring only moderate taxes.

How much can taxes help selfish routing

Abstract: We study economic incentives for influencing selfish behavior in networks. We consider a model of selfish routing in which the latency experienced by network traffic on an edge of the network is a function of the edge congestion, and network users are assumed to selfishly route traffic on minimum-latency paths. The quality of a routing of traffic is historically measured by the sum of all travel times, also called the total latency.It is well known that the outcome of selfish routing (a Nash equilibrium) does not minimize the total latency and can be improved upon with coordination, and that marginal cost pricing---charging each network user for the congestion effects caused by its presence---eliminates the inefficiency of selfish routing. However, the principle of marginal cost pricing assumes that (possibly very large) taxes cause no disutility to network users; this is appropriate only when collected taxes can be feasibly returned (directly or indirectly) to the users, for example via a lump-sum refund. If this assumption does not hold and we wish to minimize the total user disutility (latency plus taxes paid)---the total cost---how should we price the network edges? Intuition may suggest that taxes should never be able to improve the cost of a Nash equilibrium, but the famous Braess's Paradox shows this intuition to be incorrect.We consider strategies for pricing network edges to reduce the cost of a Nash equilibrium. Since levying a sufficiently large tax on an edge effectively removes it from the network, our study generalizes previous work on network design citend_hard. In this paper, we prove the following results.

Document retrieval for e-mail search and discovery using formal concept analysis

Abstract: This paper discusses a document discovery tool based on Conceptual Clustering by Formal Concept Analysis. The program allows users to navigate e-mail using a visual lattice metaphor rather than a tree. It implements a virtual. le structure over e-mail where files and entire directories can appear in multiple positions. The content and shape of the lattice formed by the conceptual ontology can assist in e-mail discovery. The system described provides more flexibility in retrieving stored e-mails than what is normally available in e-mail clients. The paper discusses how conceptual ontologies can leverage traditional document retrieval systems and aid knowledge discovery in document collections.

Overlap matching

Abstract: We propose a new paradigm for string matching, namely structural matching. In structural matching, the text and pattern contents are not important. Rather, some areas in the text and pattern, such as intervals, are singled out. A "match" is a text location where a specified relation between the text and pattern areas is satisfied. In particular we define the structural matching problem of overlap (parity) matching. We seek the text locations where all overlaps of the given pattern and text intervals have even length. We show that this problem can be solved in time O(n log m), where the text length is n and the pattern length is m. As an application of overlap matching, we show how to reduce the string matching with swaps problem to the overlap matching problem. The string matching with swaps problem is the problem of string matching in the presence of local swaps. The best deterministic upper bound known for this problem was O(nm1/3 log m log σ) for a general alphabet Σ, where σ = min(m, |Σ|). Our reduction provides a solution to the pattern matching with swaps problem in time O(n log m log σ).

Function matching: algorithms, applications, and a lower bound

Abstract: We introduce a new matching criterion - function matching - that captures several different applications. The function matching problem has as its input a text T of length n over alphabet ΣT and a pattern P = P[1]P[2] ... P[m] of length m over alphabet ΣP. We seek all text locations i for which, for some function f : ΣP → ΣT (f may also depend on i), the m-length substring that starts at i is equal to f(P[1])f(P[2]) ... f(P[m]). We give a randomized algorithm which, for any given constant k, solves the function matching problem in time O(n log n) with probability 1/nk of declaring a false positive. We give a deterministic algorithm whose time is O(n|ΣP| logm) and show that it is almost optimal in the newly formalized convolutions model. Finally, a variant of the third problem is solved by means of two-dimensional parameterized matching, for which we also give an efficient algorithm.

A fast algorithm for computing steiner edge connectivity

Abstract: Given an undirected graph or an Eulerian directed graph G and a subset S of its vertices, we show how to determine the edge connectivity C of the vertices in S in time O(C3 n log n+m). This algorithm is based on an efficient construction of tree packings which generalizes Edmonds' Theorem. These packings also yield a characterization of all minimal Steiner cuts of size C from which an efficient data structure for maintaining edge connectivity between vertices in S under edge insertion can be obtained. This data structure enables the efficient construction of a cactus tree for representing significant C-cuts among these vertices, called C-separations, in the same time bound. In turn, we use the cactus tree to give a fast implementation of an approximation algorithm for the Survivable Network Design problem due to Williamson, Goemans, Mihail and Vazirani.

Tree pattern matching to subset matching in linear time

Abstract: In this paper, we show an O(n+m) time Turing reduction from the tree pattern matching problem to another problem called the subset matching problem. Subsequent works have given efficient deterministic and randomized algorithms for the subset matching problem. Together, these works yield an O(nlog2m +m) time deterministic algorithm and an O(n log n+m) time Monte Carlo algorithm for the tree pattern matching problem.

Computing the minimum k-Cover of a string

Abstract: We study the minimum k-cover problem. For a given string x of length n and an integer k, the minimum k-cover is the minimum set of k-substrings that covers x. We show that the on-line algorithm that has been proposed by Iliopoulos and Smyth [IS92] is not correct. We prove that the problem is in fact NP-hard. Furthermore, we propose two greedy algorithms that are implemented and tested on different kind of data.

Pricing Networks with Selfish Routing

Abstract: : We study the negative consequences of selfish behavior in networks and economic means of influencing such behavior. We focus on a simple model of selfish routing, defined by Wardrop and first studied from a theoretical computer science perspective by Roughgarden and Tardos. In this model, we are given a directed network in which each edge possesses a latency function, describing the common latency (delay) experienced by all traffic on the edge as a function of the edge congestion. There is a fixed amount of traffic wishing to travel from a source vertex s to a sink vertex t, and we assume that the traffic comprises a very large population of users, so that the actions of a single individual have negligible effect on network congestion. A common way to measure the quality of an assignment of traffic to s-t paths is by the sum of all travel times the total latency. We assume that each network user acts selfishly and routes itself on a minimum-latency path, given the network congestion due to the other users. In general such a selfishly motivated assignment of traffic to paths (a Nash equilibrium) does not minimize the total latency; put differently, the outcome of selfish behavior can be improved upon with coordination.

Multidimensional matching and fast search in suffix trees

Abstract: We show how to construct a suffix tree of a text string t in linear time, after sorting the characters in the text, so that a search for pattern p take time O(p + log t), independent of the alphabet size, thereby matching the asymptotic performance of suffix arrays. Using these suffix trees or suffix arrays we then give linear time algorithms for pattern matching in any fixed dimension.