Reachability and distance queries in graphs are fundamental to numerous applications, ranging from geographic navigation systems Internet routing. Some of these applications involve huge yet require fast query answering. We propose a new data structure for representing all distances graph. The is distributed the sense that it may be viewed as assigning labels vertices, such involving vertices u v answered using only v. Our based on 2-hop covers shortest paths, or For cover collection S paths...

In the recent years, there is a growth in demand for radiofrequency (RF)-based procedures to improve skin texture, laxity and contour. The new generation of systems allow non-invasive fractional resurfacing treatments on one platform.The aim this study was evaluate safety efficacy treatment protocol using multisource RF, combining 3 different modalities each patient: [1] non-ablative RF tightening, [2] resurfacing, [3] microneedling coagulation collagen remodelling.14 subjects were enrolled...

We study the point-to-point shortest path problem in a setting where preprocessing is allowed. improve reach-based approach of Gutman [17] several ways. In particular, we introduce bidirectional version algorithm that uses implicit lower bounds and add shortcut arcs to reduce vertex reaches. Our modifications greatly both query times. The resulting as fast best previous method, due Sanders Schultes [28]. However, our simpler combines natural way with A* search, which yields significantly better

We present algorithms to label the nodes of an XML tree which is subject insertions and deletions nodes. The labeling done such that (1) we each node immediately when it inserted this remains unchanged, (2) from a pair labels alone, can decide whether one ancestor other. This problem arises in context databases support queries on structure documents as well us changes made over time. prove our assign shortest possible (up constant factor) satisfy these requirements.We also consider same...

A recent seminal result of Racke is that for any network there an oblivious routing algorithm with a polylog competitive ratio respect to congestion. Unfortunately, Racke's construction not polynomial time. We give time guarantee's bounds, and more generally gives the true optimal network.

We study the parameterized complexity of three NP-hard graph completion problems. The minimum fill-in problem asks if a can be triangulated by adding at most k edges. develop O(ck m) and O(k2mn+f(k)) algorithms for this on with n vertices m Here f(k) is exponential in constants hidden big-O notation are small do not depend k. In particular, implies that fixed-parameter tractable (FPT). proper interval problem, motivated molecular biology, made no more than show FPT providing simple...

Physical mapping is a central problem in molecular biology and the human genome project. The to reconstruct relative position of fragments DNA along from information on their pairwise overlaps. We show that four simplified models lead NP-complete decision problems: Colored unit interval graph completion, maximum (or interval) subgraph, pathwidth bipartite graph, k -consecutive ones for ≥ 2. These have been chosen reflect various features typical biological data, including false-negative...

A directed multigraph is said to be d -regular if the indegree and outdegree of every vertex exactly . By Hall's theorem, one can represent such a as combination at most n 2 cycle covers, each taken with an appropriate multiplicity. We prove that does not contain more than ⌊ d/2 ⌋ copies any 2-cycle then we find similar decomposition into pairs covers where occurs in component pair. Our proof constructive gives polynomial algorithm decomposition. Since our applications only need pair whose...

A Bottom-sketch is a summary of set items with nonnegative weights that supports approximate query processing. sketch obtained by associating each item in ground an independent random rank drawn from probability distribution depends on the weight and including k smallest value.

No abstract available.

We give a quadratic time algorithm for finding the minimum number of reversals needed to sort signed permutation. Our is faster than previous Hannenhalli and Pevzner its implementation by Berman Hannenhalli. The conceptually simple does not require special data structures. study also considerably simplifies combinatorial structures used analysis.

The success of a P2P file-sharing network highly depends on the scalability and versatility its search mechanism. Two particularly desirable features are scope (ability to find infrequent items) support for partial-match queries (queries that contain typos or include subset keywords). While centralized-index architectures (such as Napster) can both these features, existing decentralized seem at most one: prevailing unstructured protocols Gnutella FastTrack) deploy "blind" mechanism where set...

Reachability and distance queries in graphs are fundamental to numerous applications, ranging from geographic navigation systems Internet routing. Some of these applications involve huge yet require fast query answering. We propose a new data structure for representing all distances graph. The is distributed the sense that it may be viewed as assigning labels vertices, such involving vertices u v answered using only v.Our based on 2-hop covers shortest paths, or For cover collection S paths...

We consider the following problem. Give a rooted tree T, label nodes of T in most compact way such that given labels two one can determine constant time, by looking only at labels, if node is an ancestor other. The best known labeling scheme rather straightforward and uses size 2 log n, where n number vertices In tree. Our main result this paper with maximum close to 3/2 n.Our motivation for studying problem enhancing performance Web search engines. context application each indexed document...

A coreset of a point set P is small weighted points that captures some geometric properties $P$. Coresets have found use in vast host settings. We forge link between coresets, and differentially private sanitizations can answer any number queries without compromising privacy. define the notion which are simultaneously both coresets private, show how they may be constructed. first existence with low generalized sensitivity (i.e., replacing single original slightly affects quality coreset)...

The Fréchet distance measures similarity between two curves $f$ and $g$ that takes into account the ordering of points along curves: Informally, it is minimum length a leash required to connect dog, walking $f$, its owner, $g$, as they walk without backtracking their respective from one endpoint other. discrete replaces dog owner by pair frogs can only reside on $m$ $n$ specific stones, respectively. stones are in fact sequences points, typically sampled $g$. These hop stone next...

No abstract available.

We study two related problems motivated by molecular biology. • Given a graph G and constant k, does there exist supergraph $G'$ of that is unit interval has clique size at most k? proper k-coloring c G, properly colored graph? show those are polynomial for fixed k. On the other hand, we prove first problem equivalent to deciding if bandwidth $k - 1$. Hence, it NP-hard $W[t]$-hard all t. also second $W[1]$-hard t-hard. This implies both unlikely have an $O(n^\alpha )$ algorithm, where...

Motivated by a recent application in XML search engines we study the problem of labeling nodes tree (XML file) such that given labels two one can determine whether node is an ancestor other. We describe several new prefix-based schemes, where query roughly amounts to testing label prefix compare our schemes simple interval-based scheme currently used engines, as well as, with best theoretical guarantee on maximum length. performed experimental evaluation real data and some families random trees.

Several papers describe linear time algorithms to preprocess a tree, such that one can answer subsequent nearest common ancestor queries in constant time. Here, we survey these and related results. A idea used by all the for problem is solution complete binary trees straightforward. Furthermore, easily solve distributed way labeling nodes of tree from labels two alone compute label their ancestor. Whether it possible distribute data structure into short associated with important several...

Summaries of massive data sets support approximate query processing over the original data. A basic aggregate a set records is weight subpopulations specified as predicate records' attributes. Bottom-k sketches are powerful summarization format weighted items that includes priority sampling [22], and classic without replacement. They can be computed efficiently for many representations including distributed databases streams coordinated all-distances sketches. We derive novel unbiased...