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We address a version of the set-cover problem where we do not know the sets initially (and hence referred to as covert) but we can query an element to find out which sets contain this element as well as query a set to know the elements. We…
Approximate solutions to various NP-hard combinatorial optimization problems have been found by learned heuristics using complex learning models. In particular, vertex (node) classification in graphs has been a helpful method towards…
A local algorithm is a distributed algorithm where each node must operate solely based on the information that was available at system startup within a constant-size neighbourhood of the node. We study the applicability of local algorithms…
We optimally resolve the space complexity for the problem of finding an $\alpha$-approximate minimum vertex cover ($\alpha$MVC) in dynamic graph streams. We give a randomised algorithm for $\alpha$MVC which uses $O(n^2/\alpha^2)$ bits of…
This paper proposes a local search algorithm for a specific combinatorial optimisation problem in graph theory: the Hamiltonian Completion Problem (HCP) on undirected graphs. In this problem, the objective is to add as few edges as possible…
We study the communication complexity of the Minimum Vertex Cover (MVC) problem on general graphs within the \(k\)-party one-way communication model. Edges of an arbitrary \(n\)-vertex graph are distributed among \(k\) parties. The…
The Minimum Coloring Cut Problem is defined as follows: given a connected graph G with colored edges, find an edge cut E' of G (a minimal set of edges whose removal renders the graph disconnected) such that the number of colors used by the…
For both the edge deletion heuristic and the maximum-degree greedy heuristic, we study the problem of recognizing those graphs for which that heuristic can approximate the size of a minimum vertex cover within a constant factor of r, where…
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 $R_1 \setminus R_2$…
We investigate preprocessing for vertex-subset problems on graphs. While the notion of kernelization, originating in parameterized complexity theory, is a formalization of provably effective preprocessing aimed at reducing the total…
We investigate the gap between theory and practice for exact branching algorithms. In theory, branch-and-reduce algorithms currently have the best time complexity for numerous important problems. On the other hand, in practice,…
To solve the combinatorial optimization problems especially the minimal Vertex-cover problem with high efficiency, is a significant task in theoretical computer science and many other subjects. Aiming at detecting the solution space of…
The Generalized Independent Set (GIS) problem extends the classical maximum independent set problem by incorporating profits for vertices and penalties for edges. This generalized problem has been identified in diverse applications in…
It is a celebrated result in early combinatorics that, in bipartite graphs, the size of maximum matching is equal to the size of a minimum vertex cover. K\H{o}nig's proof of this fact gave an algorithm for finding a minimum vertex cover…
Near neighbor search (NNS) is a powerful abstraction for data access; however, data indexing is troublesome even for approximate indexes. For intrinsically high-dimensional data, high-quality fast searches demand either indexes with…
We show that very simple algorithms based on local search are polynomial-time approximation schemes for Maximum Independent Set, Minimum Vertex Cover and Minimum Dominating Set, when the input graphs have a fixed forbidden minor.
Given a vertex-weighted graph, the maximum weight independent set problem asks for a pair-wise non-adjacent set of vertices such that the sum of their weights is maximum. The branch-and-reduce paradigm is the de facto standard approach to…
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…
Recently similarity graphs became the leading paradigm for efficient nearest neighbor search, outperforming traditional tree-based and LSH-based methods. Similarity graphs perform the search via greedy routing: a query traverses the graph…
We analyze the query complexity of finding a local minimum in $t$ rounds on general graphs. More precisely, given a graph $G = (V,E)$ and oracle access to an unknown function $f : V \to \mathbb{R}$, the goal is to find a local minimum--a…