All posts under category "Computer Science / Data Structures"
This paper is an exploration in a functional programming framework of {em isomorphisms} between elementary data types (natural numbers, sets, multisets, finite functions, permutations binary decision diagrams, graphs, hypergraphs, parenthesis languages, dyadic rationals, primes, DNA sequences etc.)
We give an $O(n log^3 n)$ approximation scheme for Steiner forest in planar graphs, improving on the previous approximation scheme for this problem, which runs in $O(n^{f(epsilon)})$ time.
As an emerging field, MS-based proteomics still requires software tools for efficiently storing and accessing experimental data. In this work, we focus on the management of LC-MS data, which are typically made available in standard XML-based portable formats. The structures that are currently employ
We study a general class of PageRank optimization problems which consist in finding an optimal outlink strategy for a web site subject to design constraints. We consider both a continuous problem, in which one can choose the intensity of a link, and a discrete one, in which in each page, there are o
We introduce the first grammar-compressed representation of a sequence that supports searches in time that depends only logarithmically on the size of the grammar. Given a text $T[1..u]$ that is represented by a (context-free) grammar of $n$ (terminal and nonterminal) symbols and size $N$ (measured
Finding the maximum clique is a known NP-Complete problem and it is also hard to approximate. This work proposes two efficient algorithms to obtain it. Nevertheless, the first one is able to fins the maximum for some special cases, while the second one has its execution time bounded by the number of
In this paper we develop algorithms for approximating matrix multiplication with respect to the spectral norm. Let Ain{RR^{ntimes m}} and BinRR^{n times p} be two matrices and eps>0. We approximate the product A^top B using two down-sampled sketches, tilde{A}inRR^{ttimes m} and tilde{B}inRR^{ttimes
In this paper we introduce the concept of generalized d-graph (admitting cycles) as special dependency-graphs for modelling dynamic programming (DP) problems. We describe the d-graph versions of three famous single-source shortest algorithms (The algorithm based on the topological order of the verti
Delaunay and Gabriel graphs are widely studied geometric proximity structures. Motivated by applications in wireless routing, relaxed versions of these graphs known as emph{Locally Delaunay Graphs} ($LDGs$) and emph{Locally Gabriel Graphs} ($LGGs$) were proposed. We propose another generalization of
Let G be a graph cellularly embedded in a surface S. Given two closed walks c and d in G, we take advantage of the RAM model to describe linear time algorithms to decide if c and d are homotopic in S, either freely or with fixed basepoint. We restrict S to be orientable for the free homotopy test, b
We show that there exist linear-time algorithms that compute the strong chromatic index and a maximum induced matching of tree-cographs when the decomposition tree is a part of the input. We also show that there exists an efficient algorithm for the strong chromatic index of permutation graphs.
We study the problem of clock synchronization in highly dynamic networks, where communication links can appear or disappear at any time. The nodes in the network are equipped with hardware clocks, but the rate of the hardware clocks can vary arbitrarily within specific bounds, and the estimates that
We analyze the classic board game of Mastermind with $n$ holes and a constant number of colors. A result of Chv'atal (Combinatorica 3 (1983), 325-329) states that the codebreaker can find the secret code with $Theta(n / log n)$ questions. We show that this bound remains valid if the codebreaker may
We study the quantum query complexity of minor-closed graph properties, which include such problems as determining whether an $n$-vertex graph is planar, is a forest, or does not contain a path of a given length. We show that most minor-closed properties---those that cannot be characterized by a fin
We study theoretical runtime guarantees for a class of optimization problems that occur in a wide variety of inference problems. these problems are motivated by the lasso framework and have applications in machine learning and computer vision. Our work shows a close connection between these proble
Ads on the Internet are increasingly sold via ad exchanges such as RightMedia, AdECN and Doubleclick Ad Exchange. These exchanges allow real-time bidding, that is, each time the publisher contacts the exchange, the exchange ``calls out'' to solicit bids from ad networks. This aspect of soliciting bi
Predicting the occurrence of links is a fundamental problem in networks. In the link prediction problem we are given a snapshot of a network and would like to infer which interactions among existing members are likely to occur in the near future or which existing interactions are we missing. Althoug
We present a new algorithm for computing $m$-th roots over the finite field $F_q$, where $q = p^n$, with $p$ a prime, and $m$ any positive integer. In the particular case $m=2$, the cost of the new algorithm is an expected $O(M(n)log (p) + CC(n)log(n))$ operations in $F_p$, where $M(n)$ and $CC(n)$
In this paper we study the complexity of the firefighter problem and related problems on trees when more than one firefighter is available at each time step, and answer several open questions of Finbow and MacGillivray 2009. More precisely, when $b geq 2$ firefighters are allowed at each time step,
We consider greedy contention managers for transactional memory for M x N execution windows of transactions with M threads and N transactions per thread. Assuming that each transaction conflicts with at most C other transactions inside the window, a trivial greedy contention manager can schedule the
Given a set of n points in the plane, each point having a positive weight, and an integer k>0, we present an optimal O(n log n)-time deterministic algorithm to compute a step function with k steps that minimizes the maximum weighted vertical distance to the input points. It matches the expected time
Sorting is one of the most used and well investigated algorithmic problem [1]. Traditional postulation supposes the sorting data archived, and the elementary operation as comparisons of two numbers. In a view of appearance of new processors and applied problems with data streams, sorting changed its
We consider the problem of indexing a string $t$ of length $n$ to report the occurrences of a query pattern $p$ containing $m$ characters and $j$ wildcards. Let $occ$ be the number of occurrences of $p$ in $t$, and $sigma$ the size of the alphabet. We obtain the following results. - A linear space
Given a directed acyclic graph with labeled vertices, we consider the problem of finding the most common label sequences ('traces') among all paths in the graph (of some maximum length m). Since the number of paths can be huge, we propose novel algorithms whose time complexity depends only on the si
We describe a data structure that maintains the number of triangles in a dynamic undirected graph, subject to insertions and deletions of edges and of degree-zero vertices. More generally it can be used to maintain the number of copies of each possible three-vertex subgraph in time O(h) per update,
We show an improved lower bound for the Fp estimation problem in a data stream setting for p>2. A data stream is a sequence of items from the domain [n] with possible repetitions. The frequency vector x is an n-dimensional non-negative integer vector x such that x(i) is the number of occurrences of
A run is a maximal occurrence of a repetition $v$ with a period $p$ such that $2p le |v|$. The maximal number of runs in a string of length $n$ was studied by several authors and it is known to be between $0.944 n$ and $1.029 n$. We investigate highly periodic runs, in which the shortest period $p$
Motivated by the definition of linear coloring on simplicial complexes, recently introduced in the context of algebraic topology cite{Civan}, and the framework through which it was studied, we introduce the linear coloring on graphs. We provide an upper bound for the chromatic number $chi(G)$, for a
Sequence representations supporting queries $access$, $select$ and $rank$ are at the core of many data structures. There is a considerable gap between the various upper bounds and the few lower bounds known for such representations, and how they relate to the space used. In this article we prove a s
The debts' clearing problem is about clearing all the debts in a group of $n$ entities (e.g. persons, companies) using a minimal number of money transaction operations. In our previous works we studied the problem, gave a dynamic programming solution solving it and proved that it is NP-hard. In this
For the most up-to-date version please visit http://www.cis.upenn.edu/~brautbar/ccgame.pdf
This paper presents a means with time complexity of at worst O(n^3) to compute the discrete logarithm on cyclic finite groups of integers modulo p. The algorithm makes use of reduction of the problem to that of finding the concurrent zeros of two periodic functions in the real numbers. The problem i
The approach mapping from a matching of bipartite graphs to digraphs has been successfully used for forcing set problem, in this paper, it is extended to uniquely restricted matching problem. We show to determine a uniquely restricted matching in a bipartite graph is equivalent to recognition a acyc
We consider the problem of choosing Euclidean points to maximize the sum of their weighted pairwise distances, when each point is constrained to a ball centered at the origin. We derive a dual minimization problem and show strong duality holds (i.e., the resulting upper bound is tight) when some loc
A $t-a$ covering array is an $mtimes n$ matrix, with entries from an alphabet of size $alpha$, such that for any choice of $t$ rows, and any ordered string of $t$ letters of the alphabet, there exists a column such that the 'values' of the rows in that column match those of the string of letters. We
The elements of a finite nonempty partially ordered set are exposed at independent uniform times in $[0,1]$ to a selector who, at any given time, can see the structure of the induced partial order on the exposed elements. The selector's task is to choose online a maximal element. This generalizes th
A pseudo-random number generator (RNG) might be used to generate w-bit random samples in d dimensions if the number of state bits is at least dw. Some RNGs perform better than others and the concept of equidistribution has been introduced in the literature in order to rank different RNGs. We define
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