hard instances

USAGE SUMMARY

The phrase "hard instances" is correct and usable in written English.
It can be used when referring to difficult or challenging examples or cases in a particular context, such as problem-solving or testing scenarios. Example: "In our research, we focused on hard instances that often lead to failure in algorithm performance."

✓ Grammatically correct

Science

Artificial Intelligence

Algorithms

Human-verified examples from authoritative sources

Exact Expressions

23 human-written examples

Hard instances of the traveling salesman problem are associated with this transition.

Artificial Intelligence

The performance of the proposed convex relaxation is evaluated on several hard instances of the UC problem.

Energy

Therefore, parallel computing is appealing to find the minimum size for hard instances in a reasonable time.

Journal of Parallel and Distributed Computing

GENET is a heuristic repair algorithm which demonstrates impressive efficiency in solving some large-scale and hard instances of constraint satisfaction problems (CSPs).

Artificial Intelligence

Graphs with high symmetry or regularity are the main source for experimentally hard instances of the notoriously difficult graph isomorphism problem.

Journal of Combinatorial Theory, Series A

The algorithm uses Benders cuts to obtain feasible home-away pattern sets in few iterations and this approach leads to significant reductions in computation time for hard instances.

European Journal of Operational Research

Human-verified similar examples from authoritative sources

Similar Expressions

37 human-written examples

However, the hardest instances are in fact concentrated at a second, lower, transition point.

Artificial Intelligence

Our recommended reformulations are well worthwhile even including overheads, especially on harder instances where solver time dominates.

Artificial Intelligence

By adding the GP stage to Hamlet, the number of solved problems increases from 58%to85%5% in the blocks world and from 50%to87%7% in the logistics domain (0%to3838% and 0%to42%2% for the hardest instances of problems considered).

Artificial Intelligence

The hardest instances were found close to the transition between regions of satisfiable and unsatisfiable instances; furthermore, unsatisfiable instances were found harder to solve than satisfiable ones.

Journal of the Brazilian Computer Society

Computing the "easiest" 90%% of all instances requires only 2.8 h; in contrast, the 1 % "hardest" instances use more than 70%% of the total computing time.

Journal of Cheminformatics

Expert writing Tips

Best practice

When describing computational problems, use "hard instances" to specifically refer to cases that push the limits of algorithms or systems.

Common error

Avoid using "hard instances" when simpler terms like "difficulties" or "challenges" suffice. "Hard instances" implies a specific, often technical, context where the difficulty is inherent to the problem's structure.

Linguistic Context

The phrase "hard instances" functions as a noun phrase where the adjective "hard" modifies the noun "instances". As Ludwig AI confirms, it refers to specific examples or cases of a problem that are particularly difficult to solve or analyze. Examples in Ludwig showcase its use across varied contexts, all denoting a high degree of difficulty.

Expression frequency: Common

Frequent in

Science

60%

Artificial Intelligence

15%

Algorithms

10%

Less common in

News & Media

5%

Formal & Business

5%

Wiki

5%

Ludwig's WRAP-UP

In summary, the phrase "hard instances" is a grammatically sound and frequently used term, especially within scientific and technical domains, as confirmed by Ludwig AI. It serves to pinpoint specific examples or cases that present significant difficulty or complexity. While alternatives like "difficult cases" or "challenging examples" exist, "hard instances" carries a precise connotation often linked to computational or mathematical problems. Its usage is primarily formal, appearing in academic papers and technical discussions, signaling a context where precision is paramount. When using "hard instances", ensure that the context aligns with this technical connotation to avoid overgeneralization.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

difficult cases

Replaces "hard" with a more common synonym, maintaining the same meaning.

challenging examples

Substitutes both words with synonyms that emphasize the demanding nature of the instances.

complex problems

Shifts the focus to the problem itself being complex rather than the instance.

tough situations

Changes the context slightly to refer to situations rather than specific instances, implying difficulty.

intractable problems

Uses a more formal term to describe problems that are difficult to solve.

demanding tasks

Focuses on tasks that require significant effort or skill.

arduous trials

Emphasizes the effort and difficulty involved in the trials or experiments.

formidable challenges

Highlights the significant and intimidating nature of the challenges.

unyielding cases

Describes instances that are resistant to solutions or change.

knotty issues

Refers to problems that are complicated and difficult to resolve.

FAQs

How can I use "hard instances" in a sentence?

You can use "hard instances" to describe particularly challenging cases or examples within a specific domain, such as "The algorithm struggled with "hard instances" of the traveling salesman problem".

What are some alternatives to saying "hard instances"?

Depending on the context, you could use alternatives like "difficult cases", "challenging examples", or "complex problems" instead of "hard instances".

In what context is it appropriate to use "hard instances"?

"Hard instances" is most appropriate in technical or academic contexts, particularly when discussing computational problems, algorithms, or mathematical challenges. It is not typically used in casual conversation.

What makes an instance "hard"?

An instance is considered "hard" when it requires significant computational resources, time, or specialized techniques to solve or analyze, often due to its inherent complexity or specific characteristics that challenge existing methods.