A note on the complexity of local search problems

Fischer, Sophie

doi:10.1016/0020-0190(94)00184-z

Cited by 22 publications

(7 citation statements)

References 4 publications

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“…The following observation underlines that finding a pure-strategy Nash equilibrium for bidirectional localeffect games with linear local-effect functions is indeed hard. It was inspired by similar results of Fischer [14] for some local search problems. Proof.…”

Section: Theorem 34 the Problem Of Deciding Whether A Weighted Netwmentioning

confidence: 99%

On the Complexity of Pure-Strategy Nash Equilibria in Congestion and Local-Effect Games

Dunkel

Schulz

2008

Mathematics of OR

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Rosenthal's congestion games constitute one of the few known classes of noncooperative games possessing pure-strategy Nash equilibria. In the network version, each player wants to route one unit of flow on a single path from her origin to her destination at minimum cost, and the cost of using an arc depends only on the total number of players using that arc. A natural extension is to allow for players controlling different amounts of flow, which results in so-called weighted congestion games. While examples have been exhibited showing that pure-strategy Nash equilibria need not exist anymore, we prove that it is actually strongly NP-hard to determine whether a given weighted network congestion game has a purestrategy Nash equilibrium. This is true regardless of whether flow is unsplittable or not. In the unsplittable case, the problem remains strongly NP-hard for a fixed number of players. In addition to congestion games, we provide complexity results on the existence and computability of pure-strategy Nash equilibria for the closely related family of bidirectional local-effect games. Therein, the cost of a player taking a particular action depends not only on the number of players choosing the same action, but also on the number of players settling for (locally) related actions.

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Section: Theorem 34 the Problem Of Deciding Whether A Weighted Netwmentioning

confidence: 99%

On the Complexity of Pure-Strategy Nash Equilibria in Congestion and Local-Effect Games

Dunkel

Schulz

2008

Mathematics of OR

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“…So far we do not have an answer to this question. We even do not know any nontrivial upper bounds on the number of moves that may be needed to reach local optimality [14][15][16][17]. In practice, we are rarely able to find a true locally optimal point because we simply do not allow the local search process run enough long time.…”

Section: Global Optimization and Computational Complexity Of Abssmentioning

confidence: 99%

Solution Attractor of Local Search System: A Method to Reduce Computational Complexity of the Traveling Salesman Problem

Li¹

2020

Novel Trends in the Traveling Salesman Problem

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The traveling salesman problem (TSP) is presumably difficult to solve exactly using local search algorithms. It can be exactly solved by only one algorithm-the enumerative search algorithm. However, the scanning of all possible solutions requires exponential computing time. Do we need exploring all the possibilities to find the optimal solution? How can we narrow down the search space effectively and efficiently for an exhausted search? This chapter attempts to answer these questions. A local search algorithm is a discrete dynamical system, in which a search trajectory searches a part of the solution space and stops at a locally optimal point. A solution attractor of a local search system for the TSP is defined as a subset of the solution space that contains all locally optimal tours. The solution attractor concept gives us great insight into the computational complexity of the TSP. If we know where the solution attractor is located in the solution space, we simply completely search the solution attractor, rather than the entire solution space, to find the globally optimal tour. This chapter describes the solution attractor of local search system for the TSP and then presents a novel search system-the attractor-based search system-that can solve the TSP much efficiently with global optimality guarantee.

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“…The EU fashion industry's primary goal is to ensure that global intellectual property rights are strengthened. 57 The easiest route to achieving this goal is likely through reaching agreements with other countries. Designers would likely gravitate to areas where design protection is strongest.…”

Section: Brexit Could Be Harmful To the European Fashion Industrymentioning

confidence: 99%

En Vogue: The Risks of Brexit to the European Fashion Industry

Esparza¹

2018

Int. J. of Lega

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Coco Channel, Yves Saint Laurent, Gianni Versace, and Thomas Burberry, all iconic names that are synonymous with fashion and the fashion industry. Further, they are all European designers. From Paris Fashion Week to Milan Fashion Week, Europe is arguably the center of emerging fashion. It can be theorized that the reason for strong intellectual property rights within the European Union (EU), in the area of fashion design, is due to the significance of the fashion industry within Europe. Within the EU, there has long been a recognition of the significance of design protection, which sets its IP protection apart from other places in the world. Several of the protections that the EU has implemented can be traced back historically to attempts by the countries in the region to protect their textile markets, and to protect regional innovations which were being developed within early textile industries. Even in the early stages of the EU's history, there were attempts to create uniformity within the area of design. The desire to create uniformity in this area is continuous, but Brexit threatens a path towards uniformity.

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A note on the complexity of local search problems

Cited by 22 publications

References 4 publications

On the Complexity of Pure-Strategy Nash Equilibria in Congestion and Local-Effect Games

On the Complexity of Pure-Strategy Nash Equilibria in Congestion and Local-Effect Games

Solution Attractor of Local Search System: A Method to Reduce Computational Complexity of the Traveling Salesman Problem

En Vogue: The Risks of Brexit to the European Fashion Industry

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