Power plays: Relationships to watch at the G-20 summit in Australia

Leaders of the 20 most powerful industrialized and developing economies are due to endorse strategies for raising global growth as they meet in Brisbane, Australia this weekend. Since they represent about two-thirds of the world's population, 85 percent of global GDP and over 75 percent of global trade, they have the heft to do so. But reaching consensus can be tricky and leaders will also be fine tuning their own myriad, complex relationships during the meeting. Here are some key relationships to keep an eye on:

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U.S.-CHINA

President Barack Obama and his Chinese counterpart Xi Jinping announced a landmark climate change agreement earlier this week in Beijing on limiting carbon emissions by the world's two largest economies. The breakthrough came after an intense two days of talks on the sidelines of the APEC summit. But that agreement and others on military cooperation and trade did not dispel the evident tensions over human rights and other issues. The U.S. is wary over China's deepening ties with Russia while Beijing is skeptical about America's moves to "pivot" strategically and economically toward Asia.

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U.S.-RUSSIA

Obama and Russian President Vladimir Putin have grappled with Russia's actions in Ukraine and other issues straining ties such as Syria and Iran in meetings on the sidelines of other summits, while putting on smiles for the cameras in the wider gatherings. Relations remain tense, as a truce between pro-Russian rebels and Ukraine's government wobbles, and the U.S. threatens to expand sanctions that have shaken the Russian economy. Putin, meanwhile, underlined his presence at the G-20 summit with the stationing of four Russian warships in international waters of Australia's northeastern coast, prompting a scathing critique from Australian prime minister Tony Abbott.

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CHINA-JAPAN

China and Japan held their first summit meeting in more than two years during the APEC gathering in Beijing this week, but the two sides remain far apart on the nagging territorial dispute over uninhabited islands in the East China Sea. Despite the frostiness apparent in Xi's reception for Japanese Prime Minister Shinzo Abe, their encounter frees the way for high-level talks on various issues, and for further expansion of business ties between Asia's two biggest economies.

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EUROPEAN UNION-REST OF THE G-20

The stalled economic recovery of the 18-nation euro common currency area will likely draw encouragement from other G-20 members for additional stimulus to help get growth back on track. European Central Bank President Mario Draghi has said the bank may begin asset purchases to pump money into the regional economy and spur inflation. Japan's recent decision to expand stimulus, and thus drive down the value of the yen, may help alleviate opposition to such stimulus from Germany, whose exports compete with Japan's.

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AUSTRALIA-INDONESIA

Tensions between the G-20 host and neighboring Indonesia, the world's biggest Muslim nation, have periodically flared in recent years, but Australian Prime Minister Tony Abbott has welcomed the recent election of Indonesian President Joko "Jokowi" Widodo. Indonesia has emerged as a leader of the Southeast Asian region, helping to mediate disputes and espousing a moderate form of Islam, but Jokowi must contend with slowing growth, endemic corruption and crumbling infrastructure.

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BRICS-REST OF THE G-20

Slowing growth in China, Brazil and Russia has cast a pall over hopes that strong growth in the BRICS (Brazil, Russia, India, China and South Africa) nations and other emerging markets might offset weakness in developed, maturing industrial nations. Weaker prices for oil and other resources are sapping vitality in many countries whose growth is heavily dependent on commodity exports. The G-20 has been working to improve price and supply information systems and to encourage infrastructure investment, among other policies to nurture the stable and inclusive development crucial for delivering on growth and jobs.