In this paper we consider the coupled task scheduling problem with exact delay times on a single machine with the objective of minimizing the total completion time of the jobs. We provide constant-factor approximation...
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The Traveling Tournament Problem (TTP) is a well-known benchmark problem in the field of tournament timetabling, which asks us to design a double round-robin schedule such that each pair of teams plays one game in eac...
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In the Strip Packing problem (SP), we are given a vertical half-strip [0, W] × [0, ∞) and a set of n axis-aligned rectangles of width at most W. The goal is to find a non-overlapping packing of all rectangles in...
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We study the generalized multidimensional bin packing problem (GVBP) that generalizes both geometric packing and vector packing. Here, we are given n rectangular items where the ith item has width w(i), height h(i), a...
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We study several questions related to diversifying search results. We give improved approximation algorithms in each of the following problems, together with some lower bounds. 1. We give a polynomial-time approximati...
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We generalize the monotone local search approach of Fomin, Gaspers, Lokshtanov and Saurabh [*** 2019], by establishing a connection between parameterized approximation and exponentialtime approximation algorithms for ...
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ISBN:
(纸本)9783959772471
We generalize the monotone local search approach of Fomin, Gaspers, Lokshtanov and Saurabh [*** 2019], by establishing a connection between parameterized approximation and exponentialtime approximation algorithms for monotone subset minimization problems. In a monotone subset minimization problem the input implicitly describes a non-empty set family over a universe of size n which is closed under taking supersets. The task is to find a minimum cardinality set in this family. Broadly speaking, we use approximate monotone local search to show that a parameterized α-approximation algorithm that runs in ck nO(1) time, where k is the solution size, can be used to derive an α-approximation randomized algorithm that runs in dn nO(1) time, where d is the unique value in ( 1, 1 + c-1 α ) such that D (1 α d-1 c-1 ) = ln c α and D (ab) is the Kullback-Leibler divergence. This running time matches that of Fomin et al. for α = 1, and is strictly better when α > 1, for any c > 1. Furthermore, we also show that this result can be derandomized at the expense of a sub-exponential multiplicative factor in the running time. We use an approximate variant of the exhaustive search as a benchmark for our algorithm. We show that the classic 2n nO(1) exhaustive search can be adapted to an α-approximate exhaustive search that runs in time (1 + exp ( -α H(1 α ))n nO(1), where H is the entropy function. Furthermore, we provide a lower bound stating that the running time of this α-approximate exhaustive search is the best achievable running time in an oracle model. When compared to approximate exhaustive search, and to other techniques, the running times obtained by approximate monotone local search are strictly better for any α ≥ 1, c > 1. We demonstrate the potential of approximate monotone local search by deriving new and faster exponential approximation algorithms for Vertex Cover, 3-Hitting Set, Directed Feedback Vertex Set, Directed Subset Feedback Vertex Set, Directed Odd Cycle Transve
Given a complete undirected graph $G=(V,E)$, where $V$ is the vertex set partitioned into $K$ \emph{clusters} $V_1,V_2,\dots,V_K$ and $E$ is the edge set with edge weights satisfying triangle inequality, and a positiv...
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Given a graph, the general problem to cover the maximum number of vertices by a collection of vertex-disjoint long paths seemingly escapes from the literature. A path containing at least k vertices is considered long....
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Recent advancements in unmanned aerial vehicles, also known as drones, have motivated logistics to use drones for multiple operations. Collaboration between drones and trucks in a last-mile delivery system has numerou...
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Multi-state system (MSS) reliability theory has received considerable popularity in the last few decades. However, only a few studies have considered the effect of stochastic dynamic environments on the deterioration ...
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