Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already declare readOnly/idempotent/openWorld/no-destroy, so the safety profile is covered. The description adds real behavioral context beyond that: the sources consulted (CLRS, NIST DADS, Skiena repository, HF Papers, arXiv), that results carry citations and dates, and that recent papers are date-filtered. It stops short of describing result counts, ordering, or how the two legs are merged.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

The purpose is front-loaded in the first clause and the remaining text is dense, information-bearing content (outputs, sources, want semantics) rather than padding. It is a long single block, but for a complex research-style tool every sentence contributes and nothing is wasted.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a complex, open-world tool with a nested constraints object and no output schema, the description covers what is returned (methods, bounds, citations, papers) and the want behavior. The constraints-fitting behavior is only in the schema, and result ordering/counts are unstated, but the agent has enough to call it correctly.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 100%, so the schema already documents all five parameters including enum values and defaults. The description mostly restates want (common vs novel) and repeats example problem strings, adding only marginal meaning beyond what the schema provides. Baseline 3 is appropriate.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific verb and resource: given a problem described in words, find algorithms/data structures/techniques that fit. The detailed output list (textbook methods, bounds, Skiena pages, arXiv/HF papers) makes the tool's role unambiguous. It does not name sibling tools (algorithm_lookup, algorithm_compare, algorithm_implementations) to draw the boundary, so it falls short of a 5.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

It explains how to invoke the tool (describe the problem in plain words, with four illustrative examples) and clarifies the want flag semantics. However there is no explicit when-not guidance and no routing to the closely-related siblings, leaving the agent to infer when algorithm_find is preferable to algorithm_lookup or algorithm_compare.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.