Related papers: Spectral Lower Bounds for Local Search
We show that a simple local search gives a PTAS for the Feedback Vertex Set (FVS) problem in minor-free graphs. An efficient PTAS in minor-free graphs was known for this problem by Fomin, Lokshtanov, Raman and Sauraubh. However, their…
This paper proposes a new framework for providing approximation guarantees of local search algorithms. Local search is a basic algorithm design technique and is widely used for various combinatorial optimization problems. To analyze local…
Spatial search occurs in a connected graph if a continuous-time quantum walk on the adjacency matrix of the graph, suitably scaled, plus a rank-one perturbation induced by any vertex will unitarily map the principal eigenvector of the graph…
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…
The Local Computation Algorithms (LCA) model is a computational model aimed at problem instances with huge inputs and output. For graph problems, the input graph is accessed using probes: strong probes (SP) specify a vertex $v$ and receive…
We propose greedy and local search algorithms for rank-constrained convex optimization, namely solving $\underset{\mathrm{rank}(A)\leq r^*}{\min}\, R(A)$ given a convex function $R:\mathbb{R}^{m\times n}\rightarrow \mathbb{R}$ and a…
Black-box complexity is a complexity theoretic measure for how difficult a problem is to be optimized by a general purpose optimization algorithm. It is thus one of the few means trying to understand which problems are tractable for genetic…
Local search is a widely used technique for tackling challenging optimization problems, offering simplicity and strong empirical performance across various problem domains. In this paper, we address the problem of scheduling a set of jobs…
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}},…
In this paper, we study the parameterized complexity of local search, whose goal is to find a good nearby solution from the given current solution. Formally, given an optimization problem where the goal is to find the largest feasible…
Given a graph $G$ and a positive integer $R$ we address the following combinatorial search theoretic problem: What is the minimum number of queries of the form "does an unknown vertex $v \in V(G)$ belong to the ball of radius $r$ around…
This work addresses approximate nearest neighbor search applied in the domain of large-scale image retrieval. Within the group testing framework we propose an efficient off-line construction of the search structures. The linear-time…
Graph partition is a key component to achieve workload balance and reduce job completion time in parallel graph processing systems. Among the various partition strategies, edge partition has demonstrated more promising performance in…
Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. We consider a relaxed version of this problem in the setting of local algorithms. The relaxation is that the constructed subgraph is a sparse spanning…
What is the effectiveness of local search algorithms for geometric problems in the plane? We prove that local search with neighborhoods of magnitude $1/\epsilon^c$ is an approximation scheme for the following problems in the Euclidian…
We present an information-theoretic approach to lower bound the oracle complexity of nonsmooth black box convex optimization, unifying previous lower bounding techniques by identifying a combinatorial problem, namely string guessing, as a…
Consider a generalization of the classical binary search problem in linearly sorted data to the graph-theoretic setting. The goal is to design an adaptive query algorithm, called a strategy, that identifies an initially unknown target…
We present new refinement heuristics for the balanced graph partitioning problem that break with an age-old rule. Traditionally, local search only permits moves that keep the block sizes balanced (below a size constraint). In this work, we…
In the present paper, we propose an efficient local search for the minimum independent dominating set problem. We consider a local search that uses $k$-swap as the neighborhood operation. Given a feasible solution $S$, it is the operation…
Local search is a fundamental optimization technique that is both widely used in practice and deeply studied in theory, yet its computational complexity remains poorly understood. The traditional frameworks, PLS and the standard algorithm…