Related papers: Spectral Lower Bounds for Local Search
The notion of vertex sparsification is introduced in \cite{M}, where it was shown that for any graph $G = (V, E)$ and a subset of $k$ terminals $K \subset V$, there is a polynomial time algorithm to construct a graph $H = (K, E_H)$ on just…
We study local computation algorithms (LCA) for maximum matching. An LCA does not return its output entirely, but reveals parts of it upon query. For matchings, each query is a vertex $v$; the LCA should return whether $v$ is matched -- and…
Nowadays, data is represented by vectors. Retrieving those vectors, among millions and billions, that are similar to a given query is a ubiquitous problem, known as similarity search, of relevance for a wide range of applications.…
The \emph{local boxicity} of a graph $G$, denoted by $lbox(G)$, is the minimum positive integer $l$ such that $G$ can be obtained using the intersection of $k$ (, where $k \geq l$,) interval graphs where each vertex of $G$ appears as a…
We generalize the monotone local search approach of Fomin, Gaspers, Lokshtanov and Saurabh [J. ACM 2019], by establishing a connection between parameterized approximation and exponential-time approximation algorithms for monotone subset…
We present a general method for obtaining strong bounds for discrete optimization problems that is based on a concept of branching duality. It can be applied when no useful integer programming model is available, and we illustrate this with…
In this paper, we study the complexity of computing locally optimal solutions for weighted versions of standard set problems such as SetCover, SetPacking, and many more. For our investigation, we use the framework of PLS, as defined in…
Local search methods can quickly find good quality solutions in cases where systematic search methods might take a large amount of time. Moreover, in the context of pattern set mining, exhaustive search methods are not applicable due to the…
A dynamic graph algorithm is a data structure that supports edge insertions, deletions, and specific problem queries. While extensive research exists on dynamic algorithms for graph problems solvable in polynomial time, most of these…
We present a complete classification of the distributed computational complexity of local optimization problems in directed cycles for both the deterministic and the randomized LOCAL model. We show that for any local optimization problem…
We prove that any Markov chain that performs local, reversible updates on randomly chosen vertices of a bounded-degree graph necessarily has mixing time at least $\Omega(n\log n)$, where $n$ is the number of vertices. Our bound applies to…
One important feature of complex systems are problem domains that have many local minima and substructure. Biological systems manage these local minima by switching between different subsystems depending on their environmental or…
In evolutionary multi-objective optimization, the indicator-based subset selection problem involves finding a subset of points that maximizes a given quality indicator. Local search is an effective approach for obtaining a high-quality…
We consider the problem of searching for an unknown target vertex $t$ in a (possibly edge-weighted) graph. Each \emph{vertex-query} points to a vertex $v$ and the response either admits $v$ is the target or provides any neighbor $s\not=v$…
Finding a maximum clique in a given graph is one of the fundamental NP-hard problems. We compare two multi-core thread-parallel adaptations of a state-of-the-art branch and bound algorithm for the maximum clique problem, and provide a novel…
A vertex set $W$ in a graph $G$ is a valid $k$-swap for a vertex cover $S$ of $G$ if $W$ has size at most $k$ and $S'=(S \setminus W) \cup (W \setminus S)$, the symmetric difference of $S$ and $W$, is a vertex cover of $G$. If $|S'| < |S|$,…
Applying local search algorithms to combinatorial optimization problems is not an easy feat. Typically, human intervention is required to compile the constraints to input data for some metaheuristic algorithm. In this paper, we establish a…
We prove lower bounds on the complexity of finding $\epsilon$-stationary points (points $x$ such that $\|\nabla f(x)\| \le \epsilon$) of smooth, high-dimensional, and potentially non-convex functions $f$. We consider oracle-based complexity…
We prove a very general lower bound technique for quantum and randomized query complexity, that is easy to prove as well as to apply. To achieve this, we introduce the use of Kolmogorov complexity to query complexity. Our technique…
Two directions in algorithms and complexity involve: (1) classifying which optimization problems can be solved in polynomial time, and (2) understanding which computational problems are hard to solve \emph{on average} in addition to the…