# Autobahn|Python WebSocket & WAMP for Python on Twisted and asyncio. [![PyPI](https://img.shields.io/pypi/v/autobahn.svg)](https://pypi.python.org/pypi/autobahn) [![Python](https://img.shields.io/pypi/pyversions/autobahn.svg)](https://pypi.python.org/pypi/autobahn) [![CI](https://github.com/crossbario/autobahn-python/workflows/main/badge.svg)](https://github.com/crossbario/autobahn-python/actions?query=workflow%3Amain) [![CI (wstest)](https://github.com/crossbario/autobahn-python/workflows/wstest/badge.svg)](https://github.com/crossbario/autobahn-python/actions?query=workflow%3Awstest) [![CD (wheels)](https://github.com/crossbario/autobahn-python/workflows/wheels/badge.svg)](https://github.com/crossbario/autobahn-python/actions?query=workflow%3Awheels) [![CD (wheels-arm64)](https://github.com/crossbario/autobahn-python/workflows/wheels-arm64/badge.svg)](https://github.com/crossbario/autobahn-python/actions?query=workflow%3Awheels-arm64) [![CD (wheels-docker)](https://github.com/crossbario/autobahn-python/workflows/wheels-docker/badge.svg)](https://github.com/crossbario/autobahn-python/actions?query=workflow%3Awheels-docker) [![Docs](https://readthedocs.org/projects/autobahn/badge/?version=latest)](https://autobahn.readthedocs.io/en/latest/) [![License](https://img.shields.io/pypi/l/autobahn.svg)](https://github.com/crossbario/autobahn-python/blob/master/LICENSE) [![Downloads](https://img.shields.io/pypi/dm/autobahn.svg)](https://pypi.python.org/pypi/autobahn) --- **Quick Links**: [Source Code](https://github.com/crossbario/autobahn-python) - [Documentation](https://autobahn.readthedocs.io/en/latest/) - [WebSocket Examples](https://autobahn.readthedocs.io/en/latest/websocket/examples.html) - [WAMP Examples](https://autobahn.readthedocs.io/en/latest/wamp/examples.html) **Community**: [Forum](https://crossbar.discourse.group/) - [StackOverflow](https://stackoverflow.com/questions/tagged/autobahn) - [Twitter](https://twitter.com/autobahnws) - [IRC \#autobahn/chat.freenode.net](https://webchat.freenode.net/) **Companion Projects**: [Autobahn|JS](https://github.com/crossbario/autobahn-js/) - [Autobahn|Cpp](https://github.com/crossbario/autobahn-cpp) - [Autobahn|Testsuite](https://github.com/crossbario/autobahn-testsuite) - [Crossbar.io](https://crossbar.io) - [WAMP](https://wamp-proto.org) ## Introduction **Autobahn|Python** is a subproject of [Autobahn](https://crossbar.io/autobahn) and provides open-source implementations of - [The WebSocket Protocol](https://tools.ietf.org/html/rfc6455) - [The Web Application Messaging Protocol (WAMP)](https://wamp-proto.org/) for Python 3.11+ and running on [Twisted](https://twistedmatrix.com/) and [asyncio](https://docs.python.org/3/library/asyncio.html). You can use **Autobahn|Python** to create clients and servers in Python speaking just plain WebSocket or WAMP. **WebSocket** allows [bidirectional real-time messaging on the Web](https://crossbario.com/blog/post/websocket-why-what-can-i-use-it/) and beyond, while [WAMP](https://wamp-proto.org/) adds real-time application communication on top of WebSocket. **WAMP** provides asynchronous **Remote Procedure Calls** and **Publish & Subscribe** for applications in _one_ protocol running over [WebSocket](https://tools.ietf.org/html/rfc6455). WAMP is a _routed_ protocol, so you need a **WAMP Router** to connect your **Autobahn|Python** based clients. We provide [Crossbar.io](https://crossbar.io), but there are [other options](https://wamp-proto.org/implementations.html#routers) as well. Note **Autobahn|Python** currently requires Python 3.11 or later. Earlier release lines supported older Python versions: up to version v19.11.2 supported Python 2 and 3.4+, up to version v20.7.1 supported Python 3.5+, and up to version v21.2.1 supported Python 3.6+. ## Features - framework for [WebSocket](https://tools.ietf.org/html/rfc6455) and [WAMP](https://wamp-proto.org/) clients and servers - runs on [CPython](https://python.org/) and PyPy <https://pypy.org/> - runs under [Twisted](https://twistedmatrix.com/) and [asyncio](https://docs.python.org/3/library/asyncio.html) - implements WebSocket [RFC6455](https://tools.ietf.org/html/rfc6455) and Draft Hybi-10+ - implements [WebSocket compression](https://tools.ietf.org/html/draft-ietf-hybi-permessage-compression) - implements [WAMP](https://wamp-proto.org/), the Web Application Messaging Protocol - high-performance, fully asynchronous implementation - best-in-class standards conformance (100% strict passes with [Autobahn Testsuite](https://crossbar.io/autobahn#testsuite): [Client](https://autobahn.ws/testsuite/reports/clients/index.html) [Server](https://autobahn.ws/testsuite/reports/servers/index.html)) - message-, frame- and streaming-APIs for WebSocket - supports TLS (secure WebSocket) and proxies - Open-source ([MIT license](https://github.com/crossbario/autobahn-python/blob/master/LICENSE)) --- ## AI Policy > **IMPORTANT: A Note on Upcoming Policy Changes Regarding AI-Assisted Content** > > Up to and including release **v25.6.1**, this project contains no code > or documentation generated with the assistance of AI tools. This version > represents the final release under our historical contribution policy. > Starting with future versions (*after* release v25.6.1), our contribution policy > will change. Subsequent releases **MAY** contain code or documentation > created with AI assistance. We urge all users and contributors to review our [AI Policy](https://github.com/crossbario/autobahn-python/blob/master/AI_POLICY.md). This document details: - The rules and warranties required for all future contributions. - The potential intellectual property implications for the project and its users. This policy was established following an open community discussion, which you can review on [GitHub issue \#1663](https://github.com/crossbario/autobahn-python/issues/1663). We are providing this transparent notice to enable you to make an informed decision. If our new AI policy is incompatible with your own (or your organization's) development practices or risk tolerance, please take this into consideration when deciding whether to upgrade beyond version v25.6.1. ## Show me some code To give you a first impression, here are two examples. We have lot more [in the repo](https://github.com/crossbario/autobahn-python/tree/master/examples). ### WebSocket Echo Server Here is a simple WebSocket Echo Server that will echo back any WebSocket message received: from autobahn.twisted.websocket import WebSocketServerProtocol # or: from autobahn.asyncio.websocket import WebSocketServerProtocol class MyServerProtocol(WebSocketServerProtocol): def onConnect(self, request): print("Client connecting: {}".format(request.peer)) def onOpen(self): print("WebSocket connection open.") def onMessage(self, payload, isBinary): if isBinary: print("Binary message received: {} bytes".format(len(payload))) else: print("Text message received: {}".format(payload.decode('utf8'))) # echo back message verbatim self.sendMessage(payload, isBinary) def onClose(self, wasClean, code, reason): print("WebSocket connection closed: {}".format(reason)) To actually run above server protocol, you need some lines of [boilerplate](https://autobahn.readthedocs.io/en/latest/websocket/programming.html#running-a-server). ### WAMP Application Component Here is a WAMP Application Component that performs all four types of actions that WAMP provides: 1. **subscribe** to a topic 2. **publish** an event 3. **register** a procedure 4. **call** a procedure from autobahn.twisted.wamp import ApplicationSession # or: from autobahn.asyncio.wamp import ApplicationSession class MyComponent(ApplicationSession): @inlineCallbacks def onJoin(self, details): # 1. subscribe to a topic so we receive events def onevent(msg): print("Got event: {}".format(msg)) yield self.subscribe(onevent, 'com.myapp.hello') # 2. publish an event to a topic self.publish('com.myapp.hello', 'Hello, world!') # 3. register a procedure for remote calling def add2(x, y): return x + y self.register(add2, 'com.myapp.add2') # 4. call a remote procedure res = yield self.call('com.myapp.add2', 2, 3) print("Got result: {}".format(res)) Above code will work on Twisted and asyncio by changing a single line (the base class of `MyComponent`). To actually run above application component, you need some lines of [boilerplate](https://autobahn.readthedocs.io/en/latest/wamp/programming.html#running-components) and a [WAMP Router](https://autobahn.readthedocs.io/en/latest/wamp/programming.html#running-a-wamp-router). ## Packaging The Autobahn|Python OSS project: - build & publish *binary wheels* on [GitHub Releases](https://github.com/crossbario/autobahn-python/releases) and [PyPI](https://pypi.org/project/autobahn/) - plans to publish on [pyx](https://astral.sh/blog/introducing-pyx) once that launches - plans to support [WheelNext](https://wheelnext.dev/) once that launches (see also: https://lwn.net/Articles/1028299/, https://labs.quansight.org/blog/python-wheels-from-tags-to-variants) - no longer bakes & publishes Docker images * - no longer explicitly supports [PyInstaller](https://pyinstaller.org/) packaging > *: for commercial users, *typedef int GmbH (Germany)*, original creator and active maintainer of Autobahn, Crossbar.io and WAMP provides production grade, optimized and supported Docker images based on RHEL 9 and Debian 12, including complete SBOM for both the base system and full Python application run-time environment based on [CycloneDX v1.6](https://cyclonedx.org/) in JSON format and as a audit-level PDF/A document fulfilling strict cybersecurity requirements addressing e.g. EU CRA and [BSI TR-03183](https://www.bsi.bund.de/DE/Themen/Unternehmen-und-Organisationen/Standards-und-Zertifizierung/Technische-Richtlinien/TR-nach-Thema-sortiert/tr03183/TR-03183_node.html). ## Package Releases Autobahn|Python publishes source distributions and pre-built wheels on [PyPI](https://pypi.org/project/autobahn/) and [GitHub Releases](https://github.com/crossbario/autobahn-python/releases). The current release line requires Python 3.11 or later and publishes wheels for CPython 3.11 through 3.14 and PyPy 3.11 across supported Linux, macOS, and Windows targets. The recommended installation method is: ```console python -m pip install autobahn ``` Pip will choose the best matching wheel for your Python implementation, operating system, and CPU architecture. See the [wheels inventory](https://autobahn.readthedocs.io/en/latest/wheels-inventory.html) for the supported wheel matrix and NVX acceleration notes. ## Extensions ### Networking framework Autobahn runs on both Twisted and asyncio. To select the respective netoworking framework, install flavor: - `asyncio`: Backwards-compatible no-op. Asyncio is included in the Python standard library for all supported Python versions. - `twisted`: Install Twisted and Twisted support in Autobahn --- ### WebSocket Acceleration and Compression #### Acceleration (Deprecated) The `accelerate` optional dependency is **no longer recommended**. Autobahn now includes **NVX** (Native Vector Extensions), which provides SIMD-accelerated native code for WebSocket operations (XOR masking and UTF-8 validation) using CFFI. See the [NVX section](#native-vector-extensions-nvx) below for details. - ~~`accelerate`~~: Deprecated - Use NVX instead #### Compression Autobahn supports multiple WebSocket per-message compression algorithms via the `compress` optional dependency: pip install autobahn[compress] **Compression Methods Available:** | Method | Availability | Standard | Implementation | Notes | |--------|--------------|----------|----------------|-------| | **permessage-deflate** | Always | [RFC 7692](https://datatracker.ietf.org/doc/html/rfc7692) | Python stdlib (zlib) | Standard WebSocket compression | | **permessage-brotli** | `[compress]` | [RFC 7932](https://datatracker.ietf.org/doc/html/rfc7932) | brotli / brotlicffi | **Recommended** - Best compression ratio | | **permessage-bzip2** | Optional | Non-standard | Python stdlib (bz2) | Requires Python built with libbz2 | | **permessage-snappy** | Manual install | Non-standard | python-snappy | Requires separate installation | **Platform-Optimized Brotli Support:** Autobahn includes **Brotli compression** with full binary wheel coverage optimized for both CPython and PyPy: - **CPython**: Uses [brotli](https://github.com/google/brotli) (Google's official package, CPyExt) - **PyPy**: Uses [brotlicffi](https://github.com/python-hyper/brotlicffi) (CFFI-based, optimized for PyPy) **Advantages of Brotli:** - **Superior compression ratio** compared to deflate or snappy - **Binary wheels** for all major platforms (Linux x86_64/ARM64, macOS x86_64/ARM64, Windows x86_64) - **IETF standard** ([RFC 7932](https://datatracker.ietf.org/doc/html/rfc7932)) for HTTP compression - **Fast decompression** suitable for real-time applications - **Widely adopted** by browsers and CDNs **Resources:** - [RFC 7932 - Brotli Compressed Data Format](https://datatracker.ietf.org/doc/html/rfc7932) - [Google Brotli](https://github.com/google/brotli) - Official implementation - [brotlicffi](https://github.com/python-hyper/brotlicffi) - CFFI bindings for PyPy - [PyPI: brotlicffi](https://pypi.org/project/brotlicffi/) - [WAMP Brotli Extension Discussion](https://github.com/wamp-proto/wamp-proto/issues/555) **Note on Snappy:** [Snappy](https://github.com/google/snappy) compression is available but requires manual installation of [python-snappy](https://pypi.org/project/python-snappy/) (no binary wheels): pip install python-snappy # Requires libsnappy-dev system library For most use cases, **Brotli is recommended** over Snappy due to better compression ratios and included binary wheels. --- ### Encryption and WAMP authentication Autobahn supports running over TLS (for WebSocket and all WAMP transports) as well as **WAMP-cryposign** authentication. To install use this flavor: - `encryption`: Installs TLS and WAMP-cryptosign dependencies Autobahn also supports **WAMP-SCRAM** authentication. To install: - `scram`: Installs WAMP-SCRAM dependencies --- ### Native vector extensions (NVX) > This is NOT yet complete - ALPHA! Autobahn contains **NVX**, a network accelerator library that provides SIMD accelerated native vector code for WebSocket (XOR masking) and UTF-8 validation. > NVX lives in namespace > autobahn.nvx and currently > requires a x86-86 CPU with at least SSE2 and makes use of > SSE4.1 if available. The code is written using vector > instrinsics, should compile with both GCC and Clang,and > interfaces with Python using CFFI, and hence runs fast on PyPy. --- ### WAMP Serializers **The JSON, MessagePack, CBOR and FlatBuffers serializers are included by default** - batteries included! UBJSON is available via the optional `autobahn[serialization]` extra. Autobahn|Python ships with the following WAMP serializers: - **JSON** (standard library) - always available - **MessagePack** - high-performance binary serialization - **CBOR** - IETF standard binary serialization (RFC 8949) - **UBJSON** - Universal Binary JSON *(optional: `pip install autobahn[serialization]`)* - **Flatbuffers** - Google's zero-copy serialization (vendored) #### Architecture & Performance The serializer dependencies are optimized for both **CPython** and **PyPy**: | Serializer | CPython | PyPy | Wheel Type | Notes | |------------|---------|------|------------|-------| | **json** | stdlib | stdlib | - | Always available | | **msgpack** | Binary wheel (C extension) | u-msgpack-python (pure Python) | Native + Universal | PyPy JIT makes pure Python faster than C | | **ujson** | Binary wheel | Binary wheel | Native | Available for both implementations | | **cbor2** | Binary wheel | Pure Python fallback | Native + Universal | Binary wheels + py3-none-any | | **ubjson** *(optional)* | C ext (from sdist) | ❌ n/a (CPython only) | Source only — no wheels | Optional `autobahn[serialization]` extra (bjdata, pulls numpy). CPython-only: bjdata can't install on PyPy ([NeuroJSON/pybj#6](https://github.com/NeuroJSON/pybj/issues/6)); on PyPy use cbor/msgpack. On CPython without a compiler set `PYBJDATA_NO_EXTENSION=1` | | **flatbuffers** | Vendored | Vendored | Included | Always available, no external dependency | **Key Design Principles:** 1. **Batteries Included**: Core serializers (JSON, MessagePack, CBOR, FlatBuffers) available without extra install steps; UBJSON via the optional `autobahn[serialization]` extra 2. **PyPy Optimization**: Pure Python implementations leverage PyPy's JIT for superior performance 3. **Binary Wheels**: Native wheels for all major platforms (Linux x86_64/ARM64, macOS x86_64/ARM64, Windows x86_64) 4. **Zero System Pollution**: All dependencies install cleanly via wheels or pure Python 5. **WAMP Compliance**: Full protocol support out-of-the-box **Total Additional Size**: ~590KB (negligible compared to full application install) #### Platform Coverage All serializer dependencies provide binary wheels for: - **Linux**: x86_64, ARM64 (manylinux, musllinux) - **macOS**: x86_64 (Intel), ARM64 (Apple Silicon) - **Windows**: x86_64 (AMD64), ARM64 - **Python**: 3.11, 3.12, 3.13, 3.14 (including 3.14t free-threaded) - **Implementations**: CPython, PyPy 3.11+ #### Backwards Compatibility The `serialization` optional dependency is maintained for backwards compatibility: pip install autobahn[serialization] # Still works, but now a no-op #### ujson Acceleration To speed up JSON on CPython using the faster `ujson`, set: AUTOBAHN_USE_UJSON=1 > **Warning**: Using `ujson` will break the ability of Autobahn to transport and translate binary application payloads in WAMP transparently. This ability depends on features of the standard library `json` module not available in `ujson`. #### Recommendations - **General use**: JSON (stdlib) or CBOR - **High performance**: MessagePack or Flatbuffers - **Strict standards**: CBOR (IETF RFC 8949) - **Zero-copy**: Flatbuffers (for large payloads) --- ## Dependency Analysis **Autobahn|Python is fully optimized for both CPython and PyPy with comprehensive binary wheel coverage.** All dependencies follow these design principles: 1. **CFFI over CPyExt**: All native extensions use CFFI for optimal PyPy compatibility 2. **Binary Wheels First**: Native wheels available for all major platforms 3. **PyPy-Optimized**: Platform-specific packages leverage PyPy's JIT compiler 4. **Zero System Pollution**: No system libraries or build tools required for installation ### Core Dependencies | Dependency | Purpose | CPython | PyPy | Wheel Coverage | Notes | |------------|---------|---------|------|----------------|-------| | **txaio** | Twisted/asyncio abstraction | Universal wheel | Universal wheel | ✅ Excellent | Pure Python, works everywhere | | **cryptography** | TLS, X.509, cryptographic primitives | Binary wheel (Rust+CFFI) | Binary wheel (Rust+CFFI) | ✅ Excellent | 40+ wheels per release | | **hyperlink** | URL parsing | Universal wheel | Universal wheel | ✅ Excellent | Pure Python | ### WAMP Serializers (Batteries Included) All serializers **except UBJSON** are included by default in the base installation; UBJSON is an optional extra (`pip install autobahn[serialization]`): | Serializer | Purpose | CPython | PyPy | Wheel Coverage | Notes | |------------|---------|---------|------|----------------|-------| | **json** | JSON serialization | stdlib | stdlib | ✅ Always available | Python standard library | | **msgpack** | MessagePack serialization | msgpack (binary wheel) | u-msgpack-python (pure Python) | ✅ Excellent | 50+ wheels for CPython; PyPy JIT optimized | | **ujson** | Fast JSON (optional) | Binary wheel | Binary wheel | ✅ Excellent | 30+ wheels; both implementations | | **cbor2** | CBOR serialization (RFC 8949) | Binary wheel | Pure Python fallback | ✅ Excellent | 30+ binary wheels + universal fallback | | **bjdata** | UBJSON serialization *(optional)* | C ext (from sdist) | ❌ n/a (CPython only) | ⚠️ sdist only — no wheels | `autobahn[serialization]` extra; pulls numpy. CPython-only: can't install on PyPy ([NeuroJSON/pybj#6](https://github.com/NeuroJSON/pybj/issues/6)). On CPython without a compiler set `PYBJDATA_NO_EXTENSION=1`. For wheels-only/cross-arch/PyPy installs prefer cbor/msgpack | | **flatbuffers** | Google Flatbuffers | **Vendored** | **Vendored** | ✅ Perfect | Included in our wheel, zero external dependency | ### Optional: Twisted Framework Available via `pip install autobahn[twisted]`: | Dependency | Purpose | CPython | PyPy | Wheel Coverage | Notes | |------------|---------|---------|------|----------------|-------| | **zope.interface** | Component architecture | Binary wheel | Binary wheel | ✅ Excellent | 40+ wheels | | **twisted** | Async networking framework | Universal wheel | Universal wheel | ✅ Excellent | Pure Python | | **attrs** | Class attributes | Universal wheel | Universal wheel | ✅ Excellent | Pure Python | ### Optional: WebSocket Compression Available via `pip install autobahn[compress]`: | Compression Method | CPython | PyPy | Wheel Coverage | Standards | Notes | |-------------------|---------|------|----------------|-----------|-------| | **permessage-deflate** | stdlib (zlib) | stdlib (zlib) | ✅ Always available | RFC 7692 | Python standard library | | **permessage-brotli** | brotli (CPyExt) | brotlicffi (CFFI) | ✅ Excellent | RFC 7932 | 40+ wheels (brotli), 20+ wheels (brotlicffi) | | **permessage-bzip2** | stdlib (bz2) | stdlib (bz2) | ✅ Always available | Non-standard | Python standard library | | **permessage-snappy** | python-snappy (optional) | python-snappy (optional) | ⚠️ No wheels | Non-standard | Manual install; requires libsnappy-dev | **Recommendation**: Use **permessage-brotli** for optimal compression with full binary wheel support. ### Optional: Encryption & WAMP Authentication Available via `pip install autobahn[encryption]`: | Dependency | Purpose | CPython | PyPy | Wheel Coverage | Notes | |------------|---------|---------|------|----------------|-------| | **pyopenssl** | TLS/SSL operations | Universal wheel | Universal wheel | ✅ Excellent | Pure Python wrapper | | **service-identity** | TLS service verification | Universal wheel | Universal wheel | ✅ Excellent | Pure Python | | **pynacl** | NaCl cryptography | Binary wheel (CFFI) | Binary wheel (CFFI) | ✅ Excellent | 30+ CFFI wheels | | **pytrie** | Trie data structure | Universal wheel | Universal wheel | ✅ Excellent | Pure Python | | **qrcode** | QR code generation | Universal wheel | Universal wheel | ✅ Excellent | Pure Python | | **base58** | Base58 encoding | Universal wheel | Universal wheel | ✅ Excellent | Pure Python | | **ecdsa** | ECDSA signatures | Universal wheel | Universal wheel | ✅ Excellent | Pure Python | ### Optional: WAMP-SCRAM Authentication Available via `pip install autobahn[scram]`: | Dependency | Purpose | CPython | PyPy | Wheel Coverage | Notes | |------------|---------|---------|------|----------------|-------| | **cffi** | C Foreign Function Interface | Binary wheel | Binary wheel | ✅ Excellent | 40+ wheels including PyPy | | **argon2-cffi** | Argon2 password hashing | Binary wheel (CFFI) | Binary wheel (CFFI) | ✅ Excellent | 30+ CFFI wheels including PyPy | | **passlib** | Password hashing framework | Universal wheel | Universal wheel | ✅ Excellent | Pure Python | ### Optional: Native Vector Extensions (NVX) Available via `pip install autobahn[nvx]`: | Feature | Implementation | CPython | PyPy | Coverage | Notes | |---------|---------------|---------|------|----------|-------| | **XOR Masking** | SIMD via CFFI | ✅ Yes | ✅ Yes | ✅ Excellent | Our own CFFI-based implementation | | **UTF-8 Validation** | SIMD via CFFI | ✅ Yes | ✅ Yes | ✅ Excellent | Our own CFFI-based implementation | **NVX** provides significant performance improvements for WebSocket operations using SIMD instructions through CFFI. ### Platform Coverage Summary **Binary wheels available for:** - **Operating Systems**: Linux (glibc/musl), macOS, Windows - **Architectures**: x86_64 (Intel/AMD), ARM64 (Apple Silicon, AWS Graviton) - **Python Versions**: 3.11, 3.12, 3.13, 3.14 (including free-threaded 3.14t) - **Implementations**: CPython, PyPy 3.11+ **All optional dependencies install cleanly without:** - System libraries (except optional python-snappy) - Build tools (gcc, make, etc.) - Package managers (apt, yum, brew) ### Verdict ✅ **Autobahn|Python achieves its goals:** 1. ✅ **Batteries Included**: All core WAMP serializers shipped by default 2. ✅ **CPython & PyPy**: Full support for both implementations 3. ✅ **CFFI Everywhere**: All native extensions use CFFI (PyPy-optimized) 4. ✅ **Binary Wheels**: Comprehensive coverage across platforms/architectures 5. ✅ **Zero System Dependencies**: Clean pip install on all platforms 6. ✅ **Performance**: Native SIMD (NVX), optimized serializers, Brotli compression **There is nothing more to optimize or wish for** - the dependency strategy is complete and optimal.