Related papers: P-SLOCAL-Completeness of Maximum Independent Set A…
The Maximal Independent Set (MIS) problem is one of the basics in the study of locality in distributed graph algorithms. This paper presents an extremely simple randomized algorithm providing a near-optimal local complexity for this…
A fundamental question is whether one can maintain a maximum independent set in polylogarithmic update time for a dynamic collection of geometric objects in Euclidean space. Already, for a set of intervals, it is known that no dynamic…
We study the problem of Covering Orthogonal Polygons with Rectangles. For polynomial-time algorithms, the best-known approximation factor is $O(\sqrt{\log n})$ when the input polygon may have holes [Kumar and Ramesh, STOC '99, SICOMP '03],…
For input $x$, let $F(x)$ denote the set of outputs that are the "legal" answers for a computational problem $F$. Suppose $x$ and members of $F(x)$ are so large that there is not time to read them in their entirety. We propose a model of…
How hard is it to find a local optimum? If we are given a graph and want to find a locally maximal cut--meaning that the number of edges in the cut can't be improved by moving a single vertex from one side to the other--then just iterating…
We extend the concept of polynomial time approximation algorithms to apply to problems for hierarchically specified graphs, many of which are PSPACE-complete. Assuming P != PSPACE, the existence or nonexistence of such efficient…
In this paper, we establish the local superlinear convergence property of some polynomial-time interior-point methods for an important family of conic optimization problems. The main structural property used in our analysis is the…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
A maximal independent set is an independent set that is not a subset of any other independent set. It is also the key problem of mathematics, computer science, and other fields. A counting problem is a type of computational problem that…
Set packing is a fundamental problem that generalises some well-known combinatorial optimization problems and knows a lot of applications. It is equivalent to hypergraph matching and it is strongly related to the maximum independent set…
We consider the hardness of approximation of optimization problems from the point of view of definability. For many NP-hard optimization problems it is known that, unless P = NP, no polynomial-time algorithm can give an approximate solution…
In the Maximum Independent Set of Objects problem, we are given an $n$-vertex planar graph $G$ and a family $\mathcal{D}$ of $N$ objects, where each object is a connected subgraph of $G$. The task is to find a subfamily $\mathcal{F}…
For any $\varepsilon > 0$, we give a polynomial-time $n^\varepsilon$-approximation algorithm for Max Independent Set in graphs of bounded twin-width given with an $O(1)$-sequence. This result is derived from the following time-approximation…
Consider the Maximum Weight Independent Set problem for rectangles: given a family of weighted axis-parallel rectangles in the plane, find a maximum-weight subset of non-overlapping rectangles. The problem is notoriously hard both in the…
We show that for every positive $\epsilon > 0$, unless NP $\subset$ BPQP, it is impossible to approximate the maximum quadratic assignment problem within a factor better than $2^{\log^{1-\epsilon} n}$ by a reduction from the maximum label…
Fixed-parameter algorithms, approximation algorithms and moderately exponential algorithms are three major approaches to algorithms design. While each of them being very active in its own, there is an increasing attention to the connection…
Recently, there has been increasing interest and progress in improvising the approximation algorithm for well-known NP-Complete problems, particularly the approximation algorithm for the Vertex-Cover problem. Here we have proposed a…
We develop an experimental algorithm for the exact solving of the maximum independent set problem. The algorithm consecutively finds the maximal independent sets of vertices in an arbitrary undirected graph such that the next such set…
Daum et al. [PODC'13] presented an algorithm that computes a maximal independent set (MIS) within $O(\log^2 n/F+\log n \mathrm{polyloglog} n)$ rounds in an $n$-node multichannel radio network with $F$ communication channels. The paper uses…
We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is…