Related papers: Towards Optimal Range Medians
Many applications require efficient management of large sets of intervals because many objects are associated with intervals (e.g., time and price intervals). In such interval management systems, range search is a primitive operator for…
We present space efficient Monte Carlo algorithms that solve Subset Sum and Knapsack instances with $n$ items using $O^*(2^{0.86n})$ time and polynomial space, where the $O^*(\cdot)$ notation suppresses factors polynomial in the input size.…
We study the problem of computing a longest increasing subsequence in a sequence $S$ of $n$ distinct elements in the presence of persistent comparison errors. In this model, every comparison between two elements can return the wrong result…
Karpinski and Nekrich (2008) introduced the problem of parameterized range majority, which asks us to preprocess a string of length $n$ such that, given the endpoints of a range, one can quickly find all the distinct elements whose relative…
In the two-dimensional orthogonal colored range counting problem, we preprocess a set, $P$, of $n$ colored points on the plane, such that given an orthogonal query rectangle, the number of distinct colors of the points contained in this…
This paper describes a linear-time algorithm that finds the longest stretch in a sequence of real numbers (``scores'') in which the sum exceeds an input parameter. The algorithm also solves the problem of finding the longest interval in…
Monotonicity is a simple yet significant qualitative characteristic. We consider the problem of segmenting an array in up to K segments. We want segments to be as monotonic as possible and to alternate signs. We propose a quality metric for…
Several biological problems require the identification of regions in a sequence where some feature occurs within a target density range: examples including the location of GC-rich regions, identification of CpG islands, and sequence…
A class of generalized conditional gradient algorithms for the solution of optimization problem in spaces of Radon measures is presented. The method iteratively inserts additional Dirac-delta functions and optimizes the corresponding…
We study the problem of $k$-means clustering in the space of straight-line segments in $\mathbb{R}^{2}$ under the Hausdorff distance. For this problem, we give a $(1+\epsilon)$-approximation algorithm that, for an input of $n$ segments, for…
Spatial range joins have many applications, including geographic information systems, location-based social networking services, neuroscience, and visualization. However, joins incur not only expensive computational costs but also too large…
In a geometric $k$-clustering problem the goal is to partition a set of points in $\mathbb{R}^d$ into $k$ subsets such that a certain cost function of the clustering is minimized. We present data structures for orthogonal range-clustering…
Given an integer array $A[1..n]$, the Range Minimum Query problem (RMQ) asks to preprocess $A$ into a data structure, supporting RMQ queries: given $a,b\in [1,n]$, return the index $i\in[a,b]$ that minimizes $A[i]$, i.e.,…
Minimal-interval semantics associates with each query over a document a set of intervals, called witnesses, that are incomparable with respect to inclusion (i.e., they form an antichain): witnesses define the minimal regions of the document…
In the semialgebraic range searching problem, we are to preprocess $n$ points in $\mathbb{R}^d$ s.t. for any query range from a family of constant complexity semialgebraic sets, all the points intersecting the range can be reported or…
A range counting problem is specified by a set $P$ of size $|P| = n$ of points in $\mathbb{R}^d$, an integer weight $x_p$ associated to each point $p \in P$, and a range space ${\cal R} \subseteq 2^{P}$. Given a query range $R \in {\cal…
For a given set of intervals on the real line, we consider the problem of ordering the intervals with the goal of minimizing an objective function that depends on the exposed interval pieces (that is, the pieces that are not covered by…
Selecting appropriate regularization coefficients is critical to performance with respect to regularized empirical risk minimization problems. Existing theoretical approaches attempt to determine the coefficients in order for regularized…
We investigate the complexity of several fundamental polynomial-time solvable problems on graphs and on matrices, when the given instance has low treewidth; in the case of matrices, we consider the treewidth of the graph formed by non-zero…
Computing the diameter, and more generally, all eccentricities of an undirected graph is an important problem in algorithmic graph theory and the challenge is to identify graph classes for which their computation can be achieved in…