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RFID tags are being used in many diverse applications in increasingly large numbers. These capabilities of these tags span from very dumb passive tags to smart active tags, with the cost of these tags correspondingly ranging from a few pennies to many dollars. One of the common problems that arise in any RFID deployment is the problem of quick estimation of the number of tags in the field up to a desired level of accuracy. Prior work in this area has focused on the identification of tags, which needs more time, and is unsuitable for many situations, especially where the tag set is dense. We take a different, more practical approach, and provide very fast and reliable estimation mechanisms. In particular, we analyze our estimation schemes and show that the time needed to estimate the number of tags in the system for a given accuracy is much better than schemes presented in related work. We show that one can estimate the cardinality of tag-sets of any size in near-constant time, for a given accuracy of estimation.

Absmct--Thls papez preseats a new algorithm for dynamic routing of bsednidth guaranteed tunneIs where tunnel routing requests arrive one-by-me Md them 19 no a priori Lwwledge regardiog future quests. Thk problem Is motivated by service provider needs for fast deployment of bandwidth guaranteed services and the consequent need ln backbone networks for fast provisioning of bandwidth guaranteed paths. Offline routing algorithms cannot be used since they require a priori knowledge ora0 tunnel Itquests that ace to be routed. Insiead, on-line algoritams that bnmdle~arrlvingoae-by-ooeaodthatsatMLasmanypoteaUal &tumdemnndS as podbkare needed. Tbe newly developed Plgolithm is an on-line aIgorSth~.~ nnd k based on the idea that a newly muted tnnnel must follow a mute that does not "interfere too muchn with a mute that may be critical to s a w a future demand. We show that this problem Is NP-bard. We then develop a path seledlon heuristic that k based on the idea of defend loading of certain %tical" links. These crlW links are MentiEd by the algorithm as links that, if heavily loaded, would make it impossible to satisfy future demands between certain ingtess-egress pah. Like mln-hop muting. the presented algorithm uses link-state inlorma-

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This paper considers the problem of determining the achievable rates in multi-hop wireless networks. We consider the problem of jointly routing the flows and scheduling transmissions to achieve a given rate vector. We develop tight necessary and sufficient conditions for the achievability of the rate vector. We develop efficient and easy to implement Fully Polynomial Time Approximation Schemes for solving the routing problem. The scheduling problem is a solved as a graph edge-coloring problem. We show that this approach guarantees that the solution obtained is within 67% of the optimal solution in the worst case and, in practice, is typically within about 80 % of the optimal solution. The approach that we use is quite flexible and is a promising method to handle more sophisticated interference conditions, multiple channels, multiple antennas, and routing with diversity requirements.

Abstract-This paper presents new algorithms for dynamic routing of bandwidth guaranteed tunnels, where tunnel routing requests arrive one by one and there is no a priori knowledge regarding future requests. This problem is motivated by service provider needs for fast deployment of bandwidth guaranteed services. Offline routing algorithms cannot be used since they require a priori knowledge of all tunnel requests that are to be routed. Instead, on-line algorithms that handle requests arriving one by one and that satisfy as many potential future demands as possible are needed. The newly developed algorithms are on-line algorithms and are based on the idea that a newly routed tunnel must follow a route that does not "interfere too much" with a route that may be critical to satisfy a future demand. We show that this problem is NP-hard. We then develop path selection heuristics which are based on the idea of deferred loading of certain "critical" links. These critical links are identified by the algorithm as links that, if heavily loaded, would make it impossible to satisfy future demands between certain ingress-egress pairs. Like min-hop routing, the presented algorithm uses link-state information and some auxiliary capacity information for path selection. Unlike previous algorithms, the proposed algorithm exploits any available knowledge of the network ingress-egress points of potential future demands, even though the demands themselves are unknown. If all nodes are ingress-egress nodes, the algorithm can still be used, particularly to reduce the rejection rate of requests between a specified subset of important ingress-egress pairs. The algorithm performs well in comparison to previously proposed algorithms on several metrics like the number of rejected demands and successful rerouting of demands upon link failure.Index Terms-Maximum flow, MPLS, optimization, quality of service routing, traffic engineering.

This paper presents new algorithms for dynamic routing of restorable bandwidth guaranteed paths. Dynamic routing implies routing of requests that arrive one-by-one with no a priori knowledge of future arrivals, and so necessitating use of on-line algorithms. Restorability implies that to successfully route a path setup request both an active path and an alternate link (node) disjoint backup path have to be routed at the same time. This joint on-line routing problem is becoming particularly important in optical networks and in MPLS (Multi Protocol Label Switching) based networks due to the trend in backbone networks toward dynamic provisioning of bandwidth guaranteed or wavelength paths. A straightforward solution for the restoration problem is to find two disjoint paths. However, this results in excessive resource usage for backup paths and does not satisfy the implicit service provider requirement of optimizing network resource utilization so as to increase the number of potential future demands that can be routed. Given a restoration objective, such as protection against single link failures, backup path bandwidth usage can be reduced by judicious sharing of backup paths amongst certain active paths while still maintaining restorability. The best sharing performance is achieved if the routing of every path in progress in the network is known to the routing algorithm at the time of a new path setup. We give an integer programming formulation for this problem which is new. Complete path routing knowledge is a reasonable assumption for a centralized routing algorithm. However, it requires maintenance of non-aggregated or per-path information which is not often desirable particularly when distributed routing is preferred. We show that a partial information scenario which uses only aggregated and not perpath information provides sufficient information for a suitably developed algorithm to be able perform almost as well as the complete information scenario. In this partial information scenario the routing algorithm only knows what fraction of each link's bandwidth, is currently used by active paths, and is currently used by backup paths. Obtaining this information is feasible using proposed traffic engineering extensions to routing protocols. We formulate the dynamic restorable bandwidth routing problem in this partial information scenario and develop efficient routing algorithms. We compare the routing performance of this algorithm to a bound obtained using complete information. Our partial information based algorithm performs very well and its performance in terms of the number of rejected requests is very close to the full information bound.

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