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We propose a new exact approach to the generalized graph layering problem that is based on a particular quadratic assignment formulation. It expresses, in a natural way, the associated layout restrictions and several possible objectives,…
There exist many variants of guarding an orthogonal polygon in an orthogonal fashion: sometimes a guard can see an entire rectangle, or along a staircase, or along an orthogonal path with at most $k$ bends. In this paper, we study all these…
In our paper, we consider the following general problems: check feasibility, count the number of feasible solutions, find an optimal solution, and count the number of optimal solutions in $P \cap Z^n$, assuming that $P$ is a polyhedron,…
In the Strip Packing problem, we are given a vertical strip of fixed width and unbounded height, along with a set of axis-parallel rectangles. The task is to place all rectangles within the strip, without overlaps, while minimizing the…
Motivated by real-world applications such as the allocation of public housing, we examine the problem of assigning a group of agents to vertices (e.g., spatial locations) of a network so that the diversity level is maximized. Specifically,…
We devise an algorithm for surveying a dynamic orthogonal polygonal domain by placing one guard at each vertex in a subset of its vertices, i.e., whenever an orthogonal polygonal domain {\cal P'} is modified to result in another orthogonal…
Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems.…
A major challenge facing existing sequential Monte-Carlo methods for parameter estimation in physics stems from the inability of existing approaches to robustly deal with experiments that have different mechanisms that yield the results…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and…
The Minimum Fill-in problem is to decide if a graph can be triangulated by adding at most k edges. Kaplan, Shamir, and Tarjan [FOCS 1994] have shown that the problem is solvable in time O(2^(O(k)) + k2 * nm) on graphs with n vertices and m…
The recommendation system is a software system to predict customers' unknown preferences from known preferences. In the recommendation system, customers' preferences are encoded into vectors, and finding the nearest vectors to each vector…
Particle filtering is a recursive Bayesian estimation technique that has gained popularity recently for tracking and localization applications. It uses Monte Carlo simulation and has proven to be a very reliable technique to model…
We address the problem of minimal actuator placement in linear systems so that the volume of the set of states reachable with one unit or less of input energy is lower bounded by a desired value. First, following the recent work of…
Given a graph $G = (V, E)$, the $3$-path partition problem is to find a minimum collection of vertex-disjoint paths each of order at most $3$ to cover all the vertices of $V$. It is different from but closely related to the well-known…
Parameterized algorithms are a very useful tool for dealing with NP-hard problems on graphs. Yet, to properly utilize parameterized algorithms it is necessary to choose the right parameter based on the type of problem and properties of the…
Traditional mathematical programming solvers require long computational times to solve constrained minimization problems of complex and large-scale physical systems. Therefore, these problems are often transformed into unconstrained ones,…
In many retrieval problems, where we must retrieve one or more entries from a gallery in response to a probe, it is common practice to learn to do by directly comparing the probe and gallery entries to one another. In many situations the…
Let $P$ be an orthogonal polygon. Consider a sliding camera that travels back and forth along an orthogonal line segment $s\in P$ as its \emph{trajectory}. The camera can see a point $p\in P$ if there exists a point $q\in s$ such that $pq$…
One of the most useful measures of cluster quality is the modularity of a partition, which measures the difference between the number of the edges joining vertices from the same cluster and the expected number of such edges in a random…