Related papers: Approximating optimization problems in graphs with…
In the matching interdiction problem, we are given an undirected graph with weights and interdiction costs on the edges and seek to remove a subset of the edges constrained to some budget, such that the weight of a maximum weight matching…
Given an undirected graph with edge costs and node weights, the minimum bisection problem asks for a partition of the nodes into two parts of equal weight such that the sum of edge costs between the parts is minimized. We give a polynomial…
We propose an exact algorithm for solving the longest simple path problem between two given vertices in undirected weighted graphs. By using graph partitioning and dynamic programming, we obtain an algorithm that is significantly faster…
We consider the problem of tracking $n$ targets in the plane using $2n$ cameras. We can use two cameras to estimate the location of a target. We are then interested in forming $n$ camera pairs where each camera belongs to exactly one pair,…
An efficient dominating set (or perfect code) in a graph is a set of vertices the closed neighborhoods of which partition the vertex set of the graph. The minimum weight efficient domination problem is the problem of finding an efficient…
We show that any submodular minimization (SM) problem defined on a linear constraint set with constraints having up to two variables per inequality, are 2-approximable in polynomial time. If the constraints are monotone (the two variables…
$\newcommand{\eps}{\varepsilon}$ In this paper, we consider two important problems defined on finite metric spaces, and provide efficient new algorithms and approximation schemes for these problems on inputs given as graph shortest path…
We present a polynomial time dynamic programming algorithm for optimal partitions in the shortest path metric induced by a tree. This resolves, among other things, the exact complexity status of the optimal partition problems in one…
We investigate the minimum cost of a wide class of combinatorial optimization problems over random bipartite geometric graphs in $\mathbb{R}^d$ where the edge cost between two points is given by a $p$-th power of their Euclidean distance.…
In a widely-studied class of multi-parametric optimization problems, the objective value of each solution is an affine function of real-valued parameters. Then, the goal is to provide an optimal solution set, i.e., a set containing an…
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…
We present a general technique for approximating bicriteria minimization problems with positive-valued, polynomially computable objective functions. Given $0<\epsilon\leq1$ and a polynomial-time $\alpha$-approximation algorithm for the…
This paper proposes a new general technique for maximal subgraph enumeration which we call proximity search, whose aim is to design efficient enumeration algorithms for problems that could not be solved by existing frameworks. To support…
We study augmenting a plane Euclidean network with a segment, called a shortcut, to minimize the largest distance between any two points along the edges of the resulting network. Problems of this type have received considerable attention…
Many problems are NP-hard and, unless P = NP, do not admit polynomial-time exact algorithms. The fastest known exact algorithms exactly usually take time exponential in the input size. Much research effort has gone into obtaining faster…
For an arbitrary tree we investigate the problems of constructing a maximum matching which minimizes or maximizes the cardinality of a maximum matching of the graph obtained from original one by its removal and present corresponding…
We study the stochastic versions of a broad class of combinatorial problems where the weights of the elements in the input dataset are uncertain. The class of problems that we study includes shortest paths, minimum weight spanning trees,…
We consider the problem of planning a collision-free path of a robot in the presence of risk zones. The robot is allowed to travel in these zones but is penalized in a super-linear fashion for consecutive accumulative time spent there. We…
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…
We show that the number of $k$-matching in a given undirected graph $G$ is equal to the number of perfect matching of the corresponding graph $G_k$ on an even number of vertices divided by a suitable factor. If $G$ is bipartite then one can…