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We propose a technique called Rotate-and-Kill for solving the polygon inclusion and circumscribing problems. By applying this technique, we obtain $O(n)$ time algorithms for computing (1) the maximum area triangle in a given $n$-sided…
We study the combinatorial complexity of D-dimensional polyhedra defined as the intersection of n halfspaces, with the property that the highest dimension of any bounded face is much smaller than D. We show that, if d is the maximum…
In this paper, we present the first outer approximation algorithm for multi-objective mixed-integer linear programming problems with any number of objectives. The algorithm also works for certain classes of non-linear programming problems.…
The skyline of a set of points in the plane is the subset of maximal points, where a point $(x,y)$ is maximal if no other point $(x',y')$ satisfies $x'\ge x$ and $y'\ge Y$. We consider the problem of preprocessing a set $P$ of $n$ points…
We present an algorithm for finding a perfect matching in a $3$-edge-connected cubic graph that intersects every $3$-edge cut in exactly one edge. Specifically, we propose an algorithm with a time complexity of $O(n \log^4 n)$, which…
Sampling edges from a graph in sublinear time is a fundamental problem and a powerful subroutine for designing sublinear-time algorithms. Suppose we have access to the vertices of the graph and know a constant-factor approximation to the…
We present a deterministic O(n log log n) time algorithm for finding shortest cycles and minimum cuts in planar graphs. The algorithm improves the previously known fastest algorithm by Italiano et al. in STOC'11 by a factor of log n. This…
There is a high demand of space-efficient algorithms in built-in or embedded softwares. In this paper, we consider the problem of designing space-efficient algorithms for computing the maximum area empty rectangle (MER) among a set of…
Let $P$ be a set of $2n$ points in the plane, and let $M_{\rm C}$ (resp., $M_{\rm NC}$) denote a bottleneck matching (resp., a bottleneck non-crossing matching) of $P$. We study the problem of computing $M_{\rm NC}$. We first prove that the…
We study a path-planning problem amid a set $\mathcal{O}$ of obstacles in $\mathbb{R}^2$, in which we wish to compute a short path between two points while also maintaining a high clearance from $\mathcal{O}$; the clearance of a point is…
Given an undirected edge-weighted graph $G=(V,E)$ with $m$ edges and $n$ vertices, the minimum cut problem asks to find a subset of vertices $S$ such that the total weight of all edges between $S$ and $V \setminus S$ is minimized. Karger's…
The area of sublinear algorithms have recently received a lot of attention. In this setting, one has to choose specific access model for the input, as the algorithm does not have time to pre-process or even to see the whole input. A…
Obeying constraints imposed by classical physics, we give optimal fine-grained algorithms for matrix multiplication and problems involving graphs and mazes, where all calculations are done in 3-dimensional space. We assume that whatever the…
For most algorithms dealing with sets of points in the plane, the only relevant information carried by the input is the combinatorial configuration of the points: the orientation of each triple of points in the set (clockwise,…
We present a new algorithm for approximating the number of triangles in a graph $G$ whose edges arrive as an arbitrary order stream. If $m$ is the number of edges in $G$, $T$ the number of triangles, $\Delta_E$ the maximum number of…
The uniqueness of an optimal solution to a combinatorial optimization problem attracts many fields of researchers' attention because it has a wide range of applications, it is related to important classes in computational complexity, and an…
The problem of solving linear systems is one of the most fundamental problems in computer science, where given a satisfiable linear system $(A,b)$, for $A \in \mathbb{R}^{n \times n}$ and $b \in \mathbb{R}^n$, we wish to find a vector $x…
We present the first near optimal approximation schemes for the maximum weighted (uncapacitated or capacitated) $b$--matching problems for non-bipartite graphs that run in time (near) linear in the number of edges. For any…
Many signal processing problems can be solved by maximizing the fitness of a segmented model over all possible partitions of the data interval. This letter describes a simple but powerful algorithm that searches the exponentially large…
We study the influence of a graph parameter called modular-width on the time complexity for optimally solving well-known polynomial problems such as Maximum Matching, Triangle Counting, and Maximum $s$-$t$ Vertex-Capacitated Flow. The…