La instalación de Visual Paradigm para UML proporciona: java.lang.NoClassDefFoundError: java.awt.Container

La instalación de Visual Paradigm para UML proporciona: java.lang.NoClassDefFoundError: java.awt.Container

Recientemente descargué Visual Paradigm para UML en mi sistema (Ubuntu 12.0.4 LTS).

Cuando intenté instalarlo, falló. Aquí está el seguimiento de la pila:

Unpacking JRE ...
Preparing JRE ...
Starting Installer ...
java.lang.NoClassDefFoundError: java.awt.Container
    at com.install4j.runtime.installer.frontend.headless.AbstractHeadlessScreenExecutor.init(Unknown Source)
    at com.install4j.runtime.installer.frontend.headless.ConsoleScreenExecutor.<init>(Unknown Source)
    at com.install4j.runtime.installer.frontend.headless.InstallerConsoleScreenExecutor.<init>(Unknown Source)
    at com.install4j.runtime.installer.Installer.getScreenExecutor(Unknown Source)
    at com.install4j.runtime.installer.Installer.runInProcess(Unknown Source)
    at com.install4j.runtime.installer.Installer.main(Unknown Source)
    at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
    at sun.reflect.NativeMethodAccessorImpl.invoke(Unknown Source)
    at sun.reflect.DelegatingMethodAccessorImpl.invoke(Unknown Source)
    at java.lang.reflect.Method.invoke(Unknown Source)
    at com.exe4j.runtime.LauncherEngine.launch(Unknown Source)
    at com.install4j.runtime.launcher.Launcher.main(Unknown Source)
java.lang.NoClassDefFoundError: java.awt.Component
    at javax.swing.ImageIcon.<clinit>(Unknown Source)
    at com.install4j.runtime.installer.frontend.GUIHelper.loadIcon(Unknown Source)
    at com.install4j.runtime.installer.frontend.GUIHelper.<clinit>(Unknown Source)
    at com.install4j.runtime.installer.helper.InstallerUtil.reportException(Unknown Source)
    at com.install4j.runtime.installer.Installer.main(Unknown Source)
    at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
    at sun.reflect.NativeMethodAccessorImpl.invoke(Unknown Source)
    at sun.reflect.DelegatingMethodAccessorImpl.invoke(Unknown Source)
    at java.lang.reflect.Method.invoke(Unknown Source)
    at com.exe4j.runtime.LauncherEngine.launch(Unknown Source)
    at com.install4j.runtime.launcher.Launcher.main(Unknown Source)

Parece que el instalador no puede encontrar una clase en la biblioteca WT. No veo cómo eso puede ser posible. ¿Alguien sabe qué está causando esto y cómo puedo solucionarlo?

[Actualizar]

java version "1.6.0_24"
OpenJDK Runtime Environment (IcedTea6 1.11.5) (6b24-1.11.5-0ubuntu1~12.04.1)
OpenJDK 64-Bit Server VM (build 20.0-b12, mixed mode)

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