For Hothouse could certainly be considered part of the "Dying Earth" sub-genre made famous by authors like Clark Ashton Smith and, of course, Jack Vance. The tale it tells takes place in the impossibly far future, when the sun has grown large and is on the verge of going supernova. Likewise, the Earth and Moon have become locked in their orbits, so that each continuously offers one face to the Sun. As if that weren't odd -- and implausible -- enough, consider this passage where Aldiss first presents the idea:
Throughout the eons, the pull of this moon had gradually slowed the axial revolution of its parent planet to a standstill, until day and night slowed, becoming fixed forever: one on one side of the planet, one on the other. At the same time, a reciprocal braking effect had checked the moon's apparent flight. Drifting farther from Earth, it had shed its role as satellite and rode along in a Trojan position, an independent planet in its own right hugging one angle of a vast equilateral triangle which held the Earth and the sun at its other angles. Now Earth and Moon, for what was left of the afternoon of eternity, faced each other in the same relative position. They were locked face to face, and so would be, until the sands of time ceased to run, or the sun ceased to shine.It's a truly evocative image, I can't deny it -- the Earth and the Moon joined to one another by cobwebs spun by spider-like plants, but, without magic or something similarly reality-shattering, I found it impossible to accept it, especially when human beings actually use these webs travel to Moon! Ultimately, I think how one reacts to such ideas will determine a lot about how one views Hothouse as a whole.
And the multitudinous strands of cable floated across the gap between them, uniting the worlds. Back and forth the traversers could shuttle at will, vegetable astronauts huge and insensible, with Earth and Luna both enmeshed in their indifferent net.
With surprising suitability, the old age of the Earth was snared about with cobwebs.
The novel tells the story of a tribe of human beings who in a vast banyan tree located within the jungle that occupies Earth's sunward face. These humans are among the few surviving animal species left on the planet, the world's ecosystem having long ago come to be dominated by plants of all sorts, many of which possess mobility, such as the aforementioned spider-like "traversers." These humans are extremely primitive, having almost no technology and similarly little knowledge of the world beyond their jungle home. Naturally, the story is about what happens when young members of the tribe are thrown on their own resources and must explore their world to survive.
Hothouse had no influence on Dungeons & Dragons so far as I can tell and understandably not. However, when the book was published in the United States, it originally carried the title The Long Afternoon of Earth, which is cited by James Ward in his introduction to the first edition of Gamma World as being a significant influence on the game. This is quite interesting on a number of levels, chiefly that Ward might have imagined the post-apocalyptic world of his RPG as being a "Dying Earth." Furthermore, I think it also shores up the notion that Ward didn't see Gamma World as hard science fiction, a notion that needs little corroboration, since the game's TSR editions always self-identified as "science fantasy." And, finally, the plot of Hothouse is about a bunch of primitive, ignorant youths (one of whom is named Gren, a name used in Gamma World itself for a species of forest-dwelling humanoid mutants) whose journeys of discovery uncover some remarkable secrets about the world they thought they inhabited. Sound familiar?
All that said, Hothouse is a very strange book, filled with some truly improbable but nevertheless imaginatively alien vistas. I'm not sure I can recommend the book on the basis of its story, let alone its science, but its imagery is often topnotch and equally useful to players and referees of "straight" fantasy as to those of science fantasy. It's not a "must read" by any measure, though it is worth looking at as an idea mine if nothing else.