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Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…
We consider the Vertex Cover problem in intersection graphs of axis-parallel rectangles on the plane. We present two algorithms: The first is an EPTAS for non-crossing rectangle families, rectangle families $\calR$ where $R_1 \setminus R_2$…
In this paper we give a f-approximation algorithm for the minimum unweighted Vertex Cover problem with Hard Capacity constraints (VCHC) on f-hypergraphs. This problem generalizes standard vertex cover for which the best known approximation…
The notion of graph covers (also referred to as locally bijective homomorphisms) plays an important role in topological graph theory and has found its computer science applications in models of local computation. For a fixed target graph…
In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…
We study the problems of covering or partitioning a polygon $P$ (possibly with holes) using a minimum number of small pieces, where a small piece is a connected sub-polygon contained in an axis-aligned unit square. For covering, we seek to…
The maximum clique problem is a well known NP-Hard problem with applications in data mining, network analysis, informatics, and many other areas. Although there exist several algorithms with acceptable runtimes for certain classes of…
The design of good heuristics or approximation algorithms for NP-hard combinatorial optimization problems often requires significant specialized knowledge and trial-and-error. Can we automate this challenging, tedious process, and learn the…
An important problem that commonly arises in areas such as internet traffic-flow analysis, phylogenetics and electrical circuit design, is to find a representation of any given metric $D$ on a finite set by an edge-weighted graph, such that…
We consider an agent seeking to obtain an item, potentially available at different locations in a physical environment. The traveling costs between locations are known in advance, but there is only probabilistic knowledge regarding the…
Heat exchanger network synthesis exploits excess heat by integrating process hot and cold streams and improves energy efficiency by reducing utility usage. Determining provably good solutions to the minimum number of matches is a bottleneck…
The Feedback vertex set with the minimum size is one of Karp's 21 NP-complete problems targeted at breaking all the cycles in a graph. This problem is applicable to a broad variety of domains, including E-commerce networks, database…
We revisit the static coverage control problem for placement of vehicles with simple motion on the real line, under the assumption that the cost is a polynomial function of the locations of the vehicles. The main contribution of this paper…
This paper describes the formal verification of NP-hardness reduction functions of two key problems relevant in algebraic lattice theory: the closest vector problem and the shortest vector problem, both in the infinity norm. The…
As robots are being integrated into our daily lives, it becomes necessary to provide guarantees on the safe and provably correct operation. Such guarantees can be provided using automata theoretic task and mission planning where the…
We show NP-completeness for several planar variants of the monotone satisfiability problem with bounded variable appearances. With one exception the presented variants have an associated bipartite graph where the vertex degree is bounded by…
The classic lower bound of Kuhn, Moscibroda and Wattenhofer [JACM 2016] states that approximate maximum matching and approximate vertex cover (among other problems) in the LOCAL model require $\Omega(\min\{\sqrt{\frac{\log n}{\log\log n}},…
The eternal vertex cover problem is a variant of the classical vertex cover problem where a set of guards on the vertices have to be dynamically reconfigured from one vertex cover to another in every round of an attacker-defender game. The…
In 1985, Chv\'{a}tal introduced the concept of star cutsets as a means to investigate the properties of perfect graphs, which inspired many researchers to study cutsets with some specific structures, for example, star cutsets, clique…
We show that a simple geometric result suffices to derive the form of the optimal solution in a large class of finite and infinite-dimensional maximum entropy problems concerning probability distributions, spectral densities and covariance…