Microsoft Corp. signed up business-software vendor SAP SE SAP 0.10% as a cloud partner, its latest effort at using alliances to challenge Inc.’s dominance in the market for web-based, on-demand computing resources.

Such tie-ups are aimed at giving big corporate customers comfort in shifting computing operations from their own data centers to companies with which they have long worked.

The Microsoft-SAP deal, expected to be announced Tuesday, is aimed at boosting Microsoft’s business known as infrastructure-as-a-service, where customers rent computing resources online.

Last year, that piece of the market hit $22.16 billion, with Amazon Web Services AMZN 0.14% accounting for 44% of it, and Microsoft’s No.

2 Azure service holding a 7.1% share, according to market-research firm Gartner Inc.

A year ago, Microsoft reached a deal with corporate-software vendor Adobe Systems Inc., in which the companies cross-promote each other’s products.

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