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In this paper we develop a procedure to deal with a family of parameter-dependent ill-posed problems, for which the exact solution in general does not exist. The original problems are relaxed by considering corresponding approximate ones,…
In this paper, we study Ranking, a well-known randomized greedy matching algorithm, for general graphs. The algorithm was originally introduced by Karp, Vazirani, and Vazirani [STOC 1990] for the online bipartite matching problem with…
Given two graphs, the graph matching problem is to align the two vertex sets so as to minimize the number of adjacency disagreements between the two graphs. The seeded graph matching problem is the graph matching problem when we are first…
We present a novel neural architecture to solve graph optimization problems where the solution consists of arbitrary node labels, allowing us to solve hard problems like graph coloring. We train our model using reinforcement learning,…
Efficient marketing or awareness-raising campaigns seek to recruit $n$ influential individuals -- where $n$ is the campaign budget -- that are able to cover a large target audience through their social connections. So far most of the…
Results on two different settings of asymptotic behavior of approximation characteristics of individual functions are presented. First, we discuss the following classical question for sparse approximation. Is it true that for any individual…
A dominating set D in a graph G is a subset of its vertices such that every vertex of the graph which does not belong to set D is adjacent to at least one vertex from set D. A set of vertices of graph G is a global dominating set if it is a…
We consider the problem of finding a minimum edge cost subgraph of a graph satisfying both given node-connectivity requirements and degree upper bounds on nodes. We present an iterative rounding algorithm of the biset LP relaxation for this…
We consider the exploration problem: an agent equipped with a depth sensor must map out a previously unknown environment using as few sensor measurements as possible. We propose an approach based on supervised learning of a greedy…
The rate of convergence of the classical Thresholding Greedy Algorithm with respect to bases is studied in this paper. We bound the error of approximation by the product of both norms -- the norm of $f$ and the $A_1$-norm of $f$. We obtain…
We consider the problem of searching for a node on a labelled random graph according to a greedy algorithm that selects a route to the desired node using metric information on the graph. Motivated by peer-to-peer networks two types of…
Many important problems in discrete optimization require maximization of a monotonic submodular function subject to matroid constraints. For these problems, a simple greedy algorithm is guaranteed to obtain near-optimal solutions. In this…
Similarity graphs are an active research direction for the nearest neighbor search (NNS) problem. New algorithms for similarity graph construction are continuously being proposed and analyzed by both theoreticians and practitioners.…
While greedy algorithms have long been observed to perform well on a wide variety of problems, up to now approximation ratios have only been known for their application to problems having submodular objective functions $f$. Since many…
We propose a theoretical framework to capture incremental solutions to cardinality constrained maximization problems. The defining characteristic of our framework is that the cardinality/support of the solution is bounded by a value…
We study the the following question in Random Graphs. We are given two disjoint sets $L,R$ with $|L|=n=\alpha m$ and $|R|=m$. We construct a random graph $G$ by allowing each $x\in L$ to choose $d$ random neighbours in $R$. The question…
It is known that greedy methods perform well for maximizing monotone submodular functions. At the same time, such methods perform poorly in the face of non-monotonicity. In this paper, we show - arguably, surprisingly - that invoking the…
We study submodular maximization problems with matroid constraints, in particular, problems where the objective can be expressed via compositions of analytic and multilinear functions. We show that for functions of this form, the so-called…
In this paper, we investigate the trade-off between convergence rate and computational cost when minimizing a composite functional with proximal-gradient methods, which are popular optimisation tools in machine learning. We consider the…
Our goal in this paper is to propose a \textit{combinatorial algorithm} that beats the only such algorithm known previously, the greedy one. We study the polynomial approximation of the Maximum Vertex Cover Problem in bipartite graphs by a…