When considering Greek tourism, it is essential to acknowledge the inherent luxury and cultural richness that saturates the nation. From white sands and sapphire waters, to the remnants of ancient civilizations, Greece is a country that encapsulates beauty and history in equal measure. Yet, when planning a dream vacation, one should not be limited to the allure of the surroundings. The choice of accommodation can significantly enhance the experience, thereby culminating in the perfect luxury vacation.

Firstly, the question arises: what exactly does one mean by a ‘luxury hotel?’ In the hospitality industry, the term 'luxury' refers to top-of-the-line comfort and opulence. This often entails not only state-of-the-art amenities, but also world-class service, exquisite gastronomy, and often, a location that offers stunning views or proximity to key attractions.

Why should one consider a luxury hotel in Greece specifically? A luxury hotel in Greece often offers more than its counterparts in other countries due to the unique blend of culture, history and geography. The country's rich heritage influences its architecture, décor, and cuisine, while its varied landscapes ensure that each hotel offers a unique experience, be it on the mainland, or one of its numerous islands.

Now that we have broadly discussed 'what' and 'why', it is time to delve into the 'how'. Booking a luxury hotel in Greece involves a multi-step process that includes research, comparison, and reservation. The first step involves identifying your personal preferences and requirements; the second necessitates thorough research, while the third and final step is securing your reservation.

Identifying your needs from your accommodation is paramount. This could range from a preference for a sea-facing room, to requiring child-friendly facilities, or even proximity to certain archaeological sites. One must also consider the hotel’s location in terms of its geographical positioning in Greece - the choices are ample, from the bustling Athens to the idyllic Santorini or the serene Crete.

Next, thorough research must be conducted. Utilizing advanced algorithms and data analytics, websites like Booking.com and TripAdvisor provide comprehensive reviews, ratings, and price comparisons. However, for a more personal touch, one might consider contacting a travel concierge service, such as Quintessentially, which provides bespoke travel advice.

Furthermore, it would be prudent to consider the hotel's commitments towards sustainable tourism. According to research conducted by the Cornell School of Hotel Administration, an increasing number of luxury travellers are influenced by a hotel’s environmental and social policies. Many luxury hotels in Greece, such as the Sani Resort in Halkidiki, have robust sustainability programs.

Finally, securing your reservation is the last step. While this process is straightforward, it is recommended to book directly through the hotel's website or a trusted travel agent. This approach assures authenticity and often yields additional benefits, such as room upgrades or complimentary services.

To conclude, hiring a luxury hotel in Greece for your dream vacation isn't simply about indulgence, it's about immersing oneself in the cultural and historical fabric of the country from the comfort of state-of-the-art facilities and services. The process may seem arduous, but the rewards, in this case, are manifold. There's a certain calculus to the decision: balancing one's personal needs with the offerings of the establishment, and the most efficient approach is a thorough one, involving research, comparison, and meticulous reservation. The pursuit of luxury, after all, is about attention to detail, and the journey to achieving that begins not at the hotel door, but right at your screen, as you start planning your perfect Greek getaway.