Esteban Feuerstein

Dynamic algorithms for shortest paths in planar graphs

Abstract We propose data structures for maintaining shortest paths in planar graphs in which the weight of an edge is modified. Our data structures allow us to compute, after an update, the shortest-path tree rooted at an arbitrary query node in time O( n log log n ) and to perform an update in O((log n ) 3 ). Our data structure can be applied also to the problem of maintaining the maximum flow problem in an s–t planar network. As far as the all-pairs shortest-path problem is concerned, we are interested in computing the shortest distances between q pairs of nodes. We show how to obtain an o( n 2 ) algorithm for computing the shortest path between q pairs of nodes whenever q = o( n 2 ). We also consider the dynamic version of the problem in which we allow the modification of the weight of an edge.

Composite Retrieval of Diverse and Complementary Bundles

Users are often faced with the problem of finding complementary items that together achieve a single common goal (e.g., a starter kit for a novice astronomer, a collection of question/answers related to low-carb nutrition, a set of places to visit on holidays). In this paper, we argue that for some application scenarios returning item bundles is more appropriate than ranked lists. Thus we define composite retrieval as the problem of finding k bundles of complementary items. Beyond complementarity of items, the bundles must be valid w.r.t. a given budget, and the answer set of k bundles must exhibit diversity. We formally define the problem and show that in its general form is NP-hard and that also the special cases in which each bundle is formed by only one item, or only one bundle is sought, are hard. Our characterization however suggests how to adopt a two-phase approach (Produce-and-Choose, or PAC) in which we first produce many valid bundles, and then we choose k among them. For the first phase we devise two ad-hoc clustering algorithms, while for the second phase we adapt heuristics with approximation guarantees for a related problem. We also devise another approach which is based on first finding a k-clustering and then selecting a valid bundle from each of the produced clusters (Cluster-and-Pick, or CAP). We compare experimentally the proposed methods on two real-world data sets: the first data set is given by a sample of touristic attractions in 10 large European cities, while the second is a large database of user-generated restaurant reviews from Yahoo! Local. Our experiments show that when diversity is highly important, CAP is the best option, while when diversity is less important, a PAC approach constructing bundles around randomly chosen pivots, is better.

Serving Requests with On-line Routing

In this paper we consider the on-line version of the routing problem with release times. Formally, it consists in a metric space M with a distinguished point o (the origin), plus a sequence of triples where pi is a point of M, ri specifies the first moment in which the request is ready to be served, and ti represents the moment in which the request is known. A server located at point o at time 0 that moves at constant unit speed must serve the sequence of requests trying to minimize the total time till all the requests are served.

On Capital Investment

We deal with the problem of making capital investments in machines for manufacturing a product. Opportunities for investment occur over time, every such option consists of a capital cost for a new machine and a resulting. productivity gain, i.e., a lower production cost for one unit of product. The goal is that of minimizing the total production and capital costs when future demand for the product being produced and investment opportunities are unknown. This can be viewed as a generalization of the ski-rental problem and related to the mortgage problem [3].

Competitive Algorithms for the On-line Traveling Salesman

In this paper the problem of efficiently serving a sequence of requests that are presented in a metric space in an on-line fashion and then returning back to the departure point is considered. The problem is the on-line version of a variant of the Traveling Salesman Problem (namely the Vehicle Routing Problem with release times), and we call it the On-Line Traveling Salesman Problem (OLTSP). It has a variety of relevant applications in logistics and robotics.

Linear time analysis of properties of conflict-free and general Petri nets

We introduce the notion of T-path within Petri nets, and propose a simple approach, based on previous work developed for directed hypergraphs, in order to determine structural properties of nets; in particular, we study the relationships between T-paths in a Petri net and _rable sequences of transitions. Let us consider a net P = hP; T; A;M0i and the set of places with a positive marking in M0, i.e., P0 = fp j M0(p) > 0g. If we regard the net as a directed graph, the existence of a simple path from any place in P0 to a transition t is, of course, a necessary condition for the potential _rability of t. This is su_cient only if the net is a State Machine, where j_tj = jt_j = 1 for all t 2 T. In this paper we show that the existence of a T-path from any subset of P0 to a transition t is a more restrictive condition and is, again, a necessary condition for the potential _rability of t. But, in this case: (a) if P is a Conict Free Petri net, this is also a su_cient condition, (b) if P is a general Petri net, t is potentially _rable by increasing the number of tokens in P0. For Conict-Free nets (CFPN) we consider the following problems: (a) determining the set of _rable transitions, (b) determining the set of reachable places, (c) determining the set of live transitions, (d) deciding the boundedness of the net. For all these problems we provide algorithms requiring linear space and time, i.e., O(jAj + jPj + jTj), for a net P = hP; T; A;M0i. Previous results for this class of networks are given by Howell, Rosier and Yen [18], providing algorithms for solving problems in Conict-Free nets in O(jPj_jTj) time and space. Given a Petri net and a marking M, the well known coverability problem consists in _nding a reachable marking M0 such that M0 _ M; this problem is known to be EXPSPACE-hard [30]. For general Petri nets we provide a partial answer to this problem. M is coverable by augmentation if it is coverable from an augmented marking M00 of the initial marking M0: M00 _ M0 and, for all p 2 P, M00(p) = 0 if M0(p) = 0. We solve this problem in linear time. The algorithms to compute T-paths are incremental: it is possible to modify the network (adding new places, transitions, arcs, tokens), and update the set of potentially _rable transitions and reachable places without recomputing them from scratch

Two-Dimensional Distributed Inverted Files

Term-partitioned indexes are generally inefficient for the evaluation of conjunctive queries, as they require the communication of long posting lists. On the other side, document-partitioned indexes incur in excessive overheads as the evaluation of every query involves the participation of all the processors, therefore their scalability is not adequate for real systems. We propose to arrange a set of processors in a two-dimensional array, applying term-partitioning at row level and document-partitioning at column level. Choosing the adequate number of rows and columns given the available number of processors, together with the selection of the proper ways of partitioning the index over that topology is the subject of this paper.

New Stochastic Algorithms for Scheduling Ads in Sponsored Search

We introduce a family of algorithms for the selection of ads in sponsored search that intends to increase the variety of choices, while not significantly reducing revenue and maintaining an incentive for advertisers to keep their bids as high as possible. Diversification of ads may be convenient for many reasons, which we also expose. Our algorithms try to distribute the available slots among all ads, using a proportional mechanism based on the bids and the expected click-through rates of the ads. Although in our experiments we used a simple first-price auction, our algorithms are compatible with strictly incentive-compatible auctions and pricing mechanisms. We have analyzed the performance of our algorithms in two different scenarios: assuming a static intrinsic click-through rate associated to each ad and in the more general case in which those rates may vary dynamically with time. Our main result is an algorithm that performs reasonably well in terms of revenue as the traditionally used, while notably increasing the diversification. In some scenarios, our newly introduced algorithms even outperform the traditional ones.

Dynamic Algorithms for Shortest Paths in Planar Graphs

We propose data structures for maintaining shortest path in planar graphs in which the weight of an edge is modified. Our data structures allow us to compute after an update the shortest-path tree rooted at an arbitrary query node in time O(n√log log n) and to perform an update in O((log n)3). Our data structure can be also applied to the problem of maintaining the maximum flow problem in an s − t planar network.

Performance Improvements for Search Systems Using an Integrated Cache of Lists+Intersections

Modern information retrieval systems use several levels of caching to speedup computation by exploiting frequent, recent or costly data used in the past. In this study we propose and evaluate a static cache that works simultaneously as list and intersection cache, offering a more efficient way of handling cache space. In addition, we propose effective strategies to select the term pairs that should populate the cache. Simulation using two datasets and a real query log reveal that the proposed approach improves overall performance in terms of total processing time, achieving savings of up to 40% in the best case.